The mathematical description of many scientific and technological problems leads to systems of partial differential equations (PDEs).

PDEs model the interactions of temporal and spatial variations of the considered physical processes. The unknowns in PDEs are functions of one or several spatial variables and, possibly, of time. In general, it is only possible to obtain approximations of the solution(s) of PDEs that are based on discretizations in space and time. A high approximation quality depends on appropriately chosen discretizations. The arising linear or non-linear systems of algebraic equations have to be solved efficiently. The research groups are working at the numerical analysis of the discretization schemes, at the implementation of these schemes, their improvement, and their further development for the application on new classes of problems. These schemes are used in the simulation of the models from applications.

The application of these methods in collaboration with partners from science and industry leads to new insight into the structure of concrete problems. This insight results in new challenges for the further development, analysis, and the numerical simulation of the considered models.


Electrolytic diode with applied potential difference in reverse bias. Depletion of ion concentration in the vicinity of the sign change of the surface charge decreases the ionic current (http://dx.doi.org/10.1002/fuce.201500215)

Publications

  Monographs

  • H.-Chr. Kaiser, D. Knees, A. Mielke, J. Rehberg, E. Rocca, M. Thomas, E. Valdinoci, eds., PDE 2015: Theory and Applications of Partial Differential Equations, 10 of Discrete and Continuous Dynamical Systems -- Series S, American Institute of Mathematical Science, Springfield, 2017, iv+933 pages, (Collection Published).
    Abstract
    HAGs von Christoph bestätigen lassen

  • P. Exner, W. König, H. Neidhardt, eds., Mathematical Results in Quantum Mechanics. Proceedings of the QMath12 Conference, World Scientific Publishing, Singapore, 2015, xii+383 pages, (Collection Published).

  • A. Zisowsky, A. Arnold, M. Ehrhardt, Th. Koprucki, Chapter 7: Transient Simulation of k$cdot$p-Schrödinger Systems Using Discrete Transparent Boundary Conditions, in: Multi-Band Effective Mass Approximations -- Advanced Mathematical Models and Numerical Techniques, M. Ehrhardt, Th. Koprucki, eds., 94 of Lecture Notes in Computational Science and Engineering, Springer, Cham et al., 2014, pp. 247--272, (Chapter Published).

  • D. Klindworth, M. Ehrhardt, Th. Koprucki, Chapter 8: Discrete Transparent Boundary Conditions for Multi-band Effective Mass Approximations, in: Multi-Band Effective Mass Approximations -- Advanced Mathematical Models and Numerical Techniques, M. Ehrhardt, Th. Koprucki, eds., 94 of Lecture Notes in Computational Science and Engineering, Springer, Cham et al., 2014, pp. 273--318, (Chapter Published).

  • M. Ehrhardt, Th. Koprucki, eds., Multi-Band Effective Mass Approximations --- Advanced Mathematical Models and Numerical Techniques, 94 of Lecture Notes in Computational Science and Engineering, Springer, Cham et al., 2014, xvi+318 pages, (Monograph Published).

  • I. Laukaityte, R. Čiegis, M. Lichtner, M. Radziunas, Parallel Numerical Algorithm for the Traveling Wave Model, in: Parallel Scientific Computing and Optimization: Advances and Applications, R. Čiegis, D. Henty, B. Kågström, J. Žilinskas, eds., 27 of Springer Optimization and Its Applications, Springer, New York, 2008, pp. 237-251, (Chapter Published).

  • M. Tlidi, R. Lefever, A.G. Vladimirov, On Vegetation Clustering, Localized Bare Soil Spots and Fairy Circles, in: Dissipative Solitons: From Optics to Biology and Medicine, N. Akhmediev, A. Ankiewicz, eds., 751 of Lecture Notes in Physics, Springer, Berlin, Heidelberg, 2008, pp. 381-402, (Chapter Published).

  • U. Bandelow, H. Gajewski, R. Hünlich, Chapter 3: Fabry--Perot Lasers: Thermodynamics-based Modeling, in: Optoelectronic Devices --- Advanced Simulation and Analysis, J. Piprek, ed., Springer, New York, 2005, pp. 63-85, (Chapter Published).

  Articles in Refereed Journals

  • P. Farrell, A. Linke, Uniform second order convergence of a complete flux scheme on unstructured 1D grids for a singularly perturbed advection-diffusion equation and some multidimensional extensions, Journal of Scientific Computing, 72 (2017), pp. 373--395, DOI 10.1007/s10915-017-0361-7 .
    Abstract
    The accurate and efficient discretization of singularly perturbed advection-diffusion equations on arbitrary 2D and 3D domains remains an open problem. An interesting approach to tackle this problem is the complete flux scheme (CFS) proposed by G. D. Thiart and further investigated by J. ten Thije Boonkkamp. For the CFS, uniform second order convergence has been proven on structured grids. We extend a version of the CFS to unstructured grids for a steady singularly perturbed advection-diffusion equation. By construction, the novel finite volume scheme is nodally exact in 1D for piecewise constant source terms. This property allows to use elegant continuous arguments in order to prove uniform second order convergence on unstructured one-dimensional grids. Numerical results verify the predicted bounds and suggest that by aligning the finite volume grid along the velocity field uniform second order convergence can be obtained in higher space dimensions as well.

  • M. Kantner, M. Mittnenzweig, Th. Koprucki, Hybrid quantum-classical modeling of quantum dot devices, Phys. Rev. B., 96 (2017), pp. 205301/1--205301/17, DOI 10.1103/PhysRevB.96.205301 .
    Abstract
    The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the well-established fields of semi-classical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we obtain a new hybrid quantum-classical modeling approach, which enables a comprehensive description of quantum dot devices on multiple scales: It allows the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non-)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven single-photon source based on a single quantum dot in the stationary and transient operation regime.

  • A. Linke, M. Neilan, L.G. Rebholz, N. Wilson, A connection between coupled and penalty projection timestepping schemes with FE spatial discretization for the Navier--Stokes equations, Journal of Numerical Mathematics, published online on 30.6.2016, DOI 10.1515/jnma-2016-1024 .
    Abstract
    We prove that in finite element settings where the divergence-free subspace of the velocity space has optimal approximation properties, the solution of Chorin/Temam projection methods for Navier-Stokes equations equipped with grad-div stabilization with parameter gamma, converge to the associated coupled method solution with rate 1/gamma as gamma goes to infinity. We prove this first for backward Euler schemes, and then extend the results to BDF2 schemes, and finally to schemes with outflow boundary conditions. Several numerical experiments are given which verify the convergence rate, and show how using projection methods in this setting with large grad-div stabilization parameters can dramatically improve accuracy.

  • U. Wilbrandt, C. Bartsch, N. Ahmed, N. Alia, F. Anker, L. Blank, A. Caiazzo, S. Ganesan, S. Giere, G. Matthies, R. Meesala, A. Shamim, J. Venkatensan, V. John, ParMooN -- A modernized program package based on mapped finite elements, Computers & Mathematics with Applications. An International Journal, 74 (2017), pp. 74--88, DOI 10.1016/j.camwa.2016.12.020 .

  • R. Rossi, M. Thomas, Coupling rate-independent and rate-dependent processes: Existence results, SIAM Journal on Mathematical Analysis, 49 (2017), pp. 1419--1494.
    Abstract
    We address the analysis of an abstract system coupling a rate-independet process with a second order (in time) nonlinear evolution equation. We propose suitable weak solution concepts and obtain existence results by passing to the limit in carefully devised time-discretization schemes. Our arguments combine techniques from the theory of gradient systems with the toolbox for rate-independent evolution, thus reflecting the mixed character of the problem. Finally, we discuss applications to a class of rate-independent processes in visco-elastic solids with inertia, and to a recently proposed model for damage with plasticity.

  • G.R. Barrenechea, V. John, P. Knobloch, An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes, Mathematical Models & Methods in Applied Sciences, 27 (2017), pp. 525--548, DOI 10.1142/S0218202517500087 .

  • W. Huang, L. Kamenski, On the mesh nonsingularity of the moving mesh PDE method, Mathematics of Computation, (2017), published online on 02.10.2017, DOI 10.1090/mcom/3271 .
    Abstract
    The moving mesh PDE (MMPDE) method for variational mesh generation and adaptation is studied theoretically at the discrete level, in particular the nonsingularity of the obtained meshes. Meshing functionals are discretized geometrically and the MMPDE is formulated as a modified gradient system of the corresponding discrete functionals for the location of mesh vertices. It is shown that if the meshing functional satisfies a coercivity condition, then the mesh of the semi-discrete MMPDE is nonsingular for all time if it is nonsingular initially. Moreover, the altitudes and volumes of its elements are bounded below by positive numbers depending only on the number of elements, the metric tensor, and the initial mesh. Furthermore, the value of the discrete meshing functional is convergent as time increases, which can be used as a stopping criterion in computation. Finally, the mesh trajectory has limiting meshes which are critical points of the discrete functional. The convergence of the mesh trajectory can be guaranteed when a stronger condition is placed on the meshing functional. Two meshing functionals based on alignment and equidistribution are known to satisfy the coercivity condition. The results also hold for fully discrete systems of the MMPDE provided that the time step is sufficiently small and a numerical scheme preserving the property of monotonically decreasing energy is used for the temporal discretization of the semi-discrete MMPDE. Numerical examples are presented

  • P.L. Lederer, A. Linke, Ch. Merdon, J. Schöberl, Divergence-free reconstruction operators for pressure-robust Stokes discretizations with continuous pressure finite elements, SIAM Journal on Numerical Analysis, 55 (2017), pp. 1291--1314.
    Abstract
    Classical inf-sup stable mixed finite elements for the incompressible (Navier--)Stokes equations are not pressure-robust, i.e., their velocity errors depend on the continuous pressure. How-ever, a modification only in the right hand side of a Stokes discretization is able to reestablish pressure-robustness, as shown recently for several inf-sup stable Stokes elements with discontinuous discrete pressures. In this contribution, this idea is extended to low and high order Taylor--Hood and mini elements, which have continuous discrete pressures. For the modification of the right hand side a velocity reconstruction operator is constructed that maps discretely divergence-free test functions to exactly divergence-free ones. The reconstruction is based on local H(div)-conforming flux equilibration on vertex patches, and fulfills certain orthogonality properties to provide consistency and optimal a-priori error estimates. Numerical examples for the incompressible Stokes and Navier--Stokes equations confirm that the new pressure-robust Taylor--Hood and mini elements converge with optimal order and outperform signi--cantly the classical versions of those elements when the continuous pressure is comparably large.

  • N. Ahmed, S. Becher, G. Matthies, Higher-order discontinuous Galerkin time stepping and local projection stabilization techniques for the transient Stokes problem, Computer Methods in Applied Mechanics and Engineering, 313 (2017), pp. 28--52.
    Abstract
    We introduce and analyze discontinuous Galerkin time discretizations coupled with continuous finite element methods based on equal-order interpolation in space for velocity and pressure in transient Stokes problems. Spatial stability of the pressure is ensured by adding a stabilization term based on local projection. We present error estimates for the semi-discrete problem after discretization in space only and for the fully discrete problem. The fully discrete pressure shows an instability in the limit of small time step length. Numerical tests are presented which confirm our theoretical results including the pressure instability.

  • N. Ahmed, T.Ch. Rebollo, V. John, S. Rubino, A review of variational multiscale methods for the simulation of turbulent incompressible flows, Archives of Computational Methods in Engineering. State of the Art Reviews, 24 (2017), pp. 115--164.
    Abstract
    Various realizations of variational multiscale (VMS) methods for simulating turbulent incompressible flows have been proposed in the past fifteen years. All of these realizations obey the basic principles of VMS methods: They are based on the variational formulation of the incompressible Navier--Stokes equations and the scale separation is defined by projections. However, apart from these common basic features, the various VMS methods look quite different. In this review, the derivation of the different VMS methods is presented in some detail and their relation among each other and also to other discretizations is discussed. Another emphasis consists in giving an overview about known results from the numerical analysis of the VMS methods. A few results are presented in detail to highlight the used mathematical tools. Furthermore, the literature presenting numerical studies with the VMS methods is surveyed and the obtained results are summarized.

  • N. Ahmed, T.Ch. Rebollo, V. John, S. Rubino, Analysis of a full space-time discretization of the Navier--Stokes equations by a local projection stabilization method, IMA Journal of Numerical Analysis, 37 (2017), pp. 1437--1467, DOI 10.1093/imanum/drw048 .
    Abstract
    A finite element error analysis of a local projection stabilization (LPS) method for the time-dependent Navier--Stokes equations is presented. The focus is on the high-order term-by-term stabilization method that has one level, in the sense that it is defined on a single mesh, and in which the projection-stabilized structure of standard LPS methods is replaced by an interpolation-stabilized structure. The main contribution is on proving, theoretically and numerically, the optimal convergence order of the arising fully discrete scheme. In addition, the asymptotic energy balance is obtained for slightly smooth flows. Numerical studies support the analytical results and illustrate the potential of the method for the simulation of turbulent flows. Smooth unsteady flows are simulated with optimal order of accuracy.

  • N. Ahmed, A. Linke, Ch. Merdon, Towards pressure-robust mixed methods for the incompressible Navier--Stokes equations, Computational Methods in Applied Mathematics, published online on 18.11.2017, DOI 10.1515/cmam-2017-0047 .
    Abstract
    In this contribution, classical mixed methods for the incompressible Navier-Stokes equations that relax the divergence constraint and are discretely inf-sup stable, are reviewed. Though the relaxation of the divergence constraint was claimed to be harmless since the beginning of the 1970ies, Poisson locking is just replaced by another more subtle kind of locking phenomenon, which is sometimes called poor mass conservation. Indeed, divergence-free mixed methods and classical mixed methods behave qualitatively in a different way: divergence-free mixed methods are pressure-robust, which means that, e.g., their velocity error is independent of the continuous pressure. The lack of pressure-robustness in classical mixed methods can be traced back to a consistency error of an appropriately defined discrete Helmholtz projector. Numerical analysis and numerical examples reveal that really locking-free mixed methods must be discretely inf-sup stable and pressure-robust, simultaneously. Further, a recent discovery shows that locking-free, pressure-robust mixed methods do not have to be divergence-free. Indeed, relaxing the divergence constraint in the velocity trial functions is harmless, if the relaxation of the divergence constraint in some velocity test functions is repaired, accordingly.

  • N. Ahmed, On the grad-div stabilization for the steady Oseen and Navier--Stokes equations, Calcolo. A Quarterly on Numerical Analysis and Theory of Computation, 54 (2017), pp. 471--501, DOI 10.1007/s10092-016-0194-z .
    Abstract
    This paper studies the parameter choice in the grad-div stabilization applied to the generalized problems of Oseen type. Stabilization parameters based on minimizing the H1(Ω) error of the velocity are derived which do not depend on the viscosity parameter. For the proposed parameter choices, the H1(Ω) error of the velocity is derived that shows a direct dependence on the viscosity parameter. Differences and common features to the situation for the Stokes equations are discussed. Numerical studies are presented which confirm the theoretical results. Moreover, for the Navier- Stokes equations, numerical simulations were performed on a two-dimensional ow past a circular cylinder. It turns out, for the MINI element, that the best results can be obtained without grad-div stabilization.

  • P. Farrell, Th. Koprucki, J. Fuhrmann, Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics, Journal of Computational Physics, 346 (2017), pp. 497--513, DOI 10.1016/j.jcp.2017.06.023 .
    Abstract
    For a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics we compare three thermodynamically consistent numerical fluxes known in the literature. We discuss an extension of the Scharfetter--Gummel scheme to non-Boltzmann (e.g. Fermi--Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.

  • V. John, A. Linke, Ch. Merdon, M. Neilan, L.G. Rebholz, On the divergence constraint in mixed finite element methods for incompressible flows, SIAM Review, 59 (2017), pp. 492--544, DOI 10.1137/15M1047696 .
    Abstract
    The divergence constraint of the incompressible Navier--Stokes equations is revisited in the mixed finite element framework. While many stable and convergent mixed elements have been developed throughout the past four decades, most classical methods relax the divergence constraint and only enforce the condition discretely. As a result, these methods introduce a pressure-dependent consistency error which can potentially pollute the computed velocity. These methods are not robust in the sense that a contribution from the right-hand side, which influences only the pressure in the continuous equations, impacts both velocity and pressure in the discrete equations. This paper reviews the theory and practical implications of relaxing the divergence constraint. Several approaches for improving the discrete mass balance or even for computing divergence-free solutions will be discussed: grad-div stabilization, higher order mixed methods derived on the basis of an exact de Rham complex, $bH(mathrmdiv)$-conforming finite elements, and mixed methods with an appropriate reconstruction of the test functions. Numerical examples illustrate both the potential effects of using non-robust discretizations and the improvements obtained by utilizing pressure-robust discretizations.

  • M. Liero, J. Fuhrmann, A. Glitzky, Th. Koprucki, A. Fischer, S. Reineke, 3D electrothermal simulations of organic LEDs showing negative differential resistance, Optical and Quantum Electronics, 49 (2017), pp. 330/1--330/8, DOI 10.1007/s11082-017-1167-4 .
    Abstract
    Organic semiconductor devices show a pronounced interplay between temperature-activated conductivity and self-heating which in particular causes inhomogeneities in the brightness of large-area OLEDs at high power. We consider a 3D thermistor model based on partial differential equations for the electrothermal behavior of organic devices and introduce an extension to multiple layers with nonlinear conductivity laws, which also take the diode-like behavior in recombination zones into account. We present a numerical simulation study for a red OLED using a finite-volume approximation of this model. The appearance of S-shaped current-voltage characteristics with regions of negative differential resistance in a measured device can be quantitatively reproduced. Furthermore, this simulation study reveals a propagation of spatial zones of negative differential resistance in the electron and hole transport layers toward the contact.

  • A. Linke, Ch. Merdon, W. Wollner, Optimal L2 velocity error estimate for a modified pressure-robust Crouzeix--Raviart Stokes element, IMA Journal of Numerical Analysis, 37 (2017), pp. 354--374.
    Abstract
    Recently, a novel approach for the robust discretization of the incompressible Stokes equations was proposed that slightly modifies the nonconforming Crouzeix--Raviart element such that its velocity error becomes pressure-independent. The modification results in an O(h) consistency error that allows straightforward proofs for the optimal convergence of the discrete energy norm of the velocity and of the L2 norm of the pressure. However, though the optimal convergence of the velocity in the L2 norm was observed numerically, it appeared to be nontrivial to prove. In this contribution, this gap is closed. Moreover, the dependence of the error estimates on the discrete inf-sup constant is traced in detail, which shows that classical error estimates are extremely pessimistic on domains with large aspect ratios. Numerical experiments in 2D and 3D illustrate the theoretical findings.

  • E. Meca Álvarez, A. Münch, B. Wagner, Sharp-interface formation during lithium intercalation into silicon, European Journal of Applied Mathematics, (2017), published online on 28.3.2017, DOI 10.1017/S0956792517000067 .
    Abstract
    In this study we present a phase-field model that describes the process of intercalation of Li ions into a layer of an amorphous solid such as a-Si. The governing equations couple a viscous Cahn-Hilliard-Reaction model with elasticity in the framework of the Cahn-Larché system. We discuss the parameter settings and flux conditions at the free boundary that lead to the formation of phase boundaries having a sharp gradient in ion concentration between the initial state of the solid layer and the intercalated region. We carry out a matched asymptotic analysis to derive the corresponding sharp-interface model that also takes into account the dynamics of triple points where the sharp interface in the bulk of the layer intersects the free boundary. We numerically compare the interface motion predicted by the sharp-interface model with the long-time dynamics of the phase-field model.

  • A. Mielke, M. Mittnenzweig, Convergence to equilibrium in energy-reaction-diffusion systems using vector-valued functional inequalities, Journal of Nonlinear Science, (2017), published online on 11.11.2017, DOI 10.1007/s00332-017-9427-9 .
    Abstract
    We discuss how the recently developed energy-dissipation methods for reactiondi usion systems can be generalized to the non-isothermal case. For this we use concave entropies in terms of the densities of the species and the internal energy, where the importance is that the equilibrium densities may depend on the internal energy. Using the log-Sobolev estimate and variants for lower-order entropies as well as estimates for the entropy production of the nonlinear reactions we give two methods to estimate the relative entropy by the total entropy production, namely a somewhat restrictive convexity method, which provides explicit decay rates, and a very general, but weaker compactness method.

  • K. Disser, G.P. Galdi, G. Mazzone, P. Zunino, Inertial motions of a rigid body with a cavity filled with a viscous liquid, Archive for Rational Mechanics and Analysis, 221 (2016), pp. 487--526.
    Abstract
    We consider the system of equations modeling the free motion of a rigid body with a cavity filled by a viscous (Navier-Stokes) liquid. Zhukovskiy's Theorem states that in the limit of time going to infinity, the relative fluid velocity tends to 0 and the rigid velocity of the full structure tends to a steady rotation around one of the principle axes of inertia. We give a rigorous proof of this result.
    In particular, we prove that every global weak solution in a suitable class is subject to Zhukovskiy's Theorem, and note that existence of these solutions has been established. Independently of the geometry and of parameters, this shows that the presence of fluid prevents precession of the body in the limit. In general, we cannot predict which axis will be attained, but we can show stability of the largest axis and provide criteria on the initial data which are decisive in special cases.

  • M. Kantner, Th. Koprucki, Numerical simulation of carrier transport in semiconductor devices at cryogenic temperatures, Optical and Quantum Electronics, 48 (2016), pp. 543/1--543/7.
    Abstract
    At cryogenic temperatures the electron?hole plasma in semiconductors becomes strongly degenerate, leading to very sharp internal layers, extreme depletion in intrinsic domains and strong nonlinear diffusion. As a result, the numerical simulation of the drift?diffusion system suffers from serious convergence issues using standard methods. We consider a one-dimensional p-i-n diode to illustrate these problems and present a simple temperature-embedding scheme to enable the numerical simulation at cryogenic temperatures. The method is suitable for forward-biased devices as they appear e.g. in optoelectronic applications. Moreover, the method can be applied to wide band gap semiconductors where similar numerical issues occur already at room temperature.

  • M. Kantner, U. Bandelow, Th. Koprucki, J.-H. Schulze, A. Strittmatter, H.-J. Wünsche, Efficient current injection into single quantum dots through oxide-confined pn-diodes, IEEE Transactions on Electron Devices, 63 (2016), pp. 2036--2042.
    Abstract
    Current injection into single quantum dots embedded in vertical pn-diodes featuring oxide apertures is analyzed in the low-injection regime suitable for single-photon emitters. Experimental and theoretical evidence is found for a rapid lateral spreading of the carriers after passing the oxide aperture in the conventional pin-design. By an alternative design employing p-doping up to the oxide aperture the current spreading can be suppressed resulting in an enhanced current confinement and increased injection efficiencies, both, in the continuous wave and under pulsed excitation.

  • A. Linke, G. Matthies, L. Tobiska, Robust arbitrary order mixed finite element methods for the incompressible Stokes equations with pressure independent velocity errors, ESAIM: Mathematical Modelling and Numerical Analysis, 50 (2016), pp. 289--309.
    Abstract
    Standard mixed finite element methods for the incompressible Navier-Stokes equations that relax the divergence constraint are not robust against large irrotational forces in the momentum balance and the velocity error depends on the continuous pressure. This robustness issue can be completely cured by using divergence-free mixed finite elements which deliver pressure-independent velocity error estimates. However, the construction of H1-conforming, divergence-free mixed finite element methods is rather difficult. Instead, we present a novel approach for the construction of arbitrary order mixed finite element methods which deliver pressure-independent velocity errors. The approach does not change the trial functions but replaces discretely divergence-free test functions in some operators of the weak formulation by divergence-free ones. This modification is applied to inf-sup stable conforming and nonconforming mixed finite element methods of arbitrary order in two and three dimensions. Optimal estimates for the incompressible Stokes equations are proved for the H1 and L2 errors of the velocity and the L2 error of the pressure. Moreover, both velocity errors are pressure-independent, demonstrating the improved robustness. Several numerical examples illustrate the results.

  • D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, M. Virgilio, S. Guha, Th. Schröder, G. Cappellini, Th. Koprucki, Robustness analysis of a device concept for edge-emitting lasers based on strained germanium, Optical and Quantum Electronics, 48 (2016), pp. 156/1--156/7, DOI 10.1007/s11082-016-0394-4 .
    Abstract
    We consider a device concept for edge-emitting lasers based on strained germanium microstrips. The device features an inhomogeneous tensile strain distribution generated by a SiN stressor deposited on top of the Ge microstrip. This geometry requires a lateral contact scheme and hence a full two-dimensional description. The two-dimensional simulations of the carrier transport and of the optical field, carried out in a cross section of the device orthogonal to the optical cavity, use microscopic calculations of the strained Ge material gain as an input. In this paper we study laser performance and robustness against Shockley-Read-Hall lifetime variations and device sensitivity to different strain distributions.

  • D. Peschka, N. Rotundo, M. Thomas, Towards doping optimization of semiconductor lasers, Journal of Computational and Theoretical Transport, 45 (2016), pp. 410--423.
    Abstract
    We discuss analytical and numerical methods for the optimization of optoelectronic devices by performing optimal control of the PDE governing the carrier transport with respect to the doping profile. First, we provide a cost functional that is a sum of a regularization and a contribution, which is motivated by the modal net gain that appears in optoelectronic models of bulk or quantum-well lasers. Then, we state a numerical discretization, for which we study optimized solutions for different regularizations and for vanishing weights.

  • G.R. Barrenechea, V. John, P. Knobloch, Analysis of algebraic flux correction schemes, SIAM Journal on Numerical Analysis, 54 (2016), pp. 2427--2451.
    Abstract
    A family of algebraic flux correction schemes for linear boundary value problems in any space dimension is studied. These methods' main feature is that they limit the fluxes along each one of the edges of the triangulation, and we suppose that the limiters used are symmetric. For an abstract problem, the existence of a solution, existence and uniqueness of the solution of a linearized problem, and an a priori error estimate, are proved under rather general assumptions on the limiters. For a particular (but standard in practice) choice of the limiters, it is shown that a local discrete maximum principle holds. The theory developed for the abstract problem is applied to convection-diffusion-reaction equations, where in particular an error estimate is derived. Numerical studies show its sharpness.

  • C. Bertoglio, A. Caiazzo, A Stokes-residual backflow stabilization method applied to physiological flows, Journal of Computational Physics, 313 (2016), pp. 260--278.
    Abstract
    In computational fluid dynamics incoming flow at open boundaries, or emphbackflow, often yields to unphysical instabilities for high Reynolds numbers. It is widely accepted that this is due to the incoming energy arising from the convection term, which cannot be empha priori controlled when the velocity field is unknown at the boundary. In order to improve the robustness of the numerical simulations, we propose a stabilized formulation based on a penalization of the residual of a weak Stokes problem on the open boundary, whose viscous part controls the incoming convective energy, while the inertial term contributes to the kinetic energy. We also present different strategies for the approximation of the boundary pressure gradient, which is needed for defining the stabilization term. The method has the advantage that it does not require neither artificial modifications or extensions of the computational domain. Moreover, it is consistent with the Womersley solution. We illustrate our approach on numerical examples  - both academic and real-life -  relevant to blood and respiratory flows. The results also show that the stabilization parameter can be reduced with the mesh size.

  • P. Bringmann, C. Carstensen, Ch. Merdon, Guaranteed error control for the pseudostress approximation of the Stokes equations, Numerical Methods for Partial Differential Equations. An International Journal, 32 (2016), pp. 1411--1432.
    Abstract
    The pseudostress approximation of the Stokes equations rewrites the stationary Stokes equations with pure (but possibly inhomogeneous) Dirichlet boundary conditions as another (equivalent) mixed scheme based on a stress in H(div) and the velocity in $L^2$. Any standard mixed finite element function space can be utilized for this mixed formulation, e.g. the Raviart-Thomas discretization which is related to the Crouzeix-Raviart nonconforming finite element scheme in the lowest-order case. The effective and guaranteed a posteriori error control for this nonconforming velocity-oriented discretization can be generalized to the error control of some piecewise quadratic velocity approximation that is related to the discrete pseudostress. The analysis allows for local inf-sup constants which can be chosen in a global partition to improve the estimation. Numerical examples provide strong evidence for an effective and guaranteed error control with very small overestimation factors even for domains with large anisotropy.

  • A. Ern, D. Di Pietro, A. Linke, F. Schieweck, A discontinuous skeletal method for the viscosity-dependent Stokes problem, Computer Methods in Applied Mechanics and Engineering, 306 (2016), pp. 175--195.
    Abstract
    We devise and analyze arbitrary-order nonconforming methods for the discretization of the viscosity-dependent Stokes equations on simplicial meshes. We keep track explicitly of the viscosity and aim at pressure-robust schemes that can deal with the practically relevant case of body forces with large curl-free part in a way that the discrete velocity error is not spoiled by large pressures. The method is inspired from the recent Hybrid High-Order (HHO) methods for linear elasticity. After elimination of the auxiliary variables by static condensation, the linear system to be solved involves only discrete face-based velocities, which are polynomials of degree k >=0, and cell-wise constant pressures. Our main result is a pressure-independent energy-error estimate on the velocity of order (k+1). The main ingredient to achieve pressure-independence is the use of a divergence-preserving velocity reconstruction operator in the discretization of the body forces. We also prove an L2-pressure estimate of order (k+1) and an L2-velocity estimate of order (k+2), the latter under elliptic regularity. The local mass and momentum conservation properties of the discretization are also established. Finally, two- and three-dimensional numerical results are presented to support the analysis.

  • A. Fiebach, A. Glitzky, A. Linke, Convergence of an implicit Voronoi finite volume method for reaction-diffusion problems, Numerical Methods for Partial Differential Equations. An International Journal, 32 (2016), pp. 141--174.
    Abstract
    We investigate the convergence of an implicit Voronoi finite volume method for reaction- diffusion problems including nonlinear diffusion in two space dimensions. The model allows to handle heterogeneous materials and uses the chemical potentials of the involved species as primary variables. The numerical scheme uses boundary conforming Delaunay meshes and preserves positivity and the dissipative property of the continuous system. Starting from a result on the global stability of the scheme (uniform, mesh-independent global upper and lower bounds), we prove strong convergence of the chemical activities and their gradients to a weak solution of the continuous problem. In order to illustrate the preservation of qualitative properties by the numerical scheme, we present a long-term simulation of the Michaelis-Menten-Henri system. Especially, we investigate the decay properties of the relative free energy and the evolution of the dissipation rate over several magnitudes of time, and obtain experimental orders of convergence for these quantities.

  • R. Haller-Dintelmann, A. Jonsson, D. Knees, J. Rehberg, Elliptic and parabolic regularity for second order divergence operators with mixed boundary conditions, Mathematical Methods in the Applied Sciences, 39 (2016), pp. 5007--5026, DOI 10.1002/mma.3484/abstract .
    Abstract
    We study second order equations and systems on non-Lipschitz domains including mixed boundary conditions. The key result is interpolation for suitable function spaces.

  • W. Huang, L. Kamenski, J. Lang, Stability of explicit one-step methods for P1-finite element approximation of linear diffusion equations on anisotropic meshes, SIAM Journal on Numerical Analysis, 54 (2016), pp. 1612--1634.
    Abstract
    We study the stability of explicit Runge-Kutta integration schemes for the linear finite element approximation of linear parabolic equations. The derived bound on the largest permissible time step is tight for any mesh and any diffusion matrix within a factor of 2 (d + 1), where d is the spatial dimension. Both full mass matrix and mass lumping are considered. The bound reveals that the stability condition is affected by two factors. The first one depends on the number of mesh elements and corresponds to the classic bound for the Laplace operator on a uniform mesh. The other factor reflects the effects of the interplay of the mesh geometry and the diffusion matrix. It is shown that it is not the mesh geometry itself but the mesh geometry in relation to the diffusion matrix that is crucial to the stability of explicit methods. When the mesh is uniform in the metric specified by the inverse of the diffusion matrix, the stability condition is comparable to the situation with the Laplace operator on a uniform mesh. Numerical results are presented to verify the theoretical findings.

  • M. Khodayari, P. Reinsberg, A.A. Abd-El-Latif, Ch. Merdon, J. Fuhrmann, H. Baltruschat, Determining solubility and diffusivity by using a flow cell coupled to a mass spectrometer, ChemPhysChem, 17 (2016), pp. 1647--1655.

  • N. Ahmed, G. Matthies, Numerical study of SUPG and LPS methods combined with higher order variational time discretization schemes applied to time-dependent convection-diffusion-reaction equations, Journal of Scientific Computing, 67 (2016), pp. 988--1018.
    Abstract
    This paper considers the numerical solution of time-dependent convection-diffusion-reaction equations. We shall employ combinations of streamline-upwind Petrov-Galerkin (SUPG) and local projection stabilization (LPS) methods in space with the higher order variational time discretization schemes. In particular, we consider time discretizations by discontinuous Galerkin (dG) methods and continuous Galerkin-Petrov (cGP) methods. Several numerical tests have been performed to assess the accuracy of combinations of spatial and temporal discretization schemes. Furthermore, the dependence of the results on the stabilization parameters of the spatial discretizations are discussed. Finally the long-time behavior of overshoots and undershoots is investigated.

  • A. Caiazzo, R. Guibert, I.E. Vignon-Clementel, A reduced-order modeling for efficient design study of artificial valve in enlarged ventricular outflow tracts, Computer Methods in Biomechanics and Biomedical Engineering, 19 (2016), pp. 1314--1318.
    Abstract
    A computational approach is proposed for efficient design study of a reducer stent to be percutaneously implanted in enlarged right ventricular outflow tracts (RVOT). The need for such a device is driven by the absence of bovine or artificial valves which could be implanted in these RVOT to replace the absent or incompetent native valve, as is often the case over time after Tetralogy of Fallot repair. Hemodynamics are simulated in the stented RVOT via a reduce order model based on proper orthogonal decomposition (POD), while the artificial valve is modeled as a thin resistive surface. The reduced order model is obtained from the numerical solution on a reference device configuration, then varying the geometrical parameters (diameter) for design purposes. To validate the approach, forces exerted on the valve and on the reducer are monitored, varying with geometrical parameters, and compared with the results of full CFD simulations. Such an approach could also be useful for uncertainty quantification.

  • W. Dreyer, C. Guhlke, M. Landstorfer, Theory and structure of the metal/electrolyte interface incorporating adsorption and solvation effects, Electrochimica Acta, 201 (2016), pp. 187--219.
    Abstract
    In this work we present a continuum theory for the metal/electrolyte interface which explicitly takes into account adsorption and partial solvation on the metal surface. It is based on a general theory of coupled thermo-electrodynamics for volumes and surfaces, utilized here in equilibrium and a 1D approximation. We provide explicit free energy models for the volumetric metal and electrolyte phases and derive a surface free energy for the species present on the metal surface. This surface mixture theory explicitly takes into account the very different amount of sites an adsorbate requires, originating from solvation effects on the surface. Additionally we account for electron transfer reactions on the surface and the associated stripping of the solvation shell. Based on our overall surface free energy we thus provide explicit expressions of the surface chemical potentials of all constituents. The equilibrium representations of the coverages and the overall charge are briefly summarized.

    Our model is then used to describe two examples: (i) a silver single crystal electrode with (100) face in contact to a (0.01M NaF + 0.01M KPF6) aqueous solution, and (ii) a general metal surface in contact to some electrolytic solution AC for which an electron transfer reaction occurs in the potential range of interest. We reflect the actual modeling procedure for these examples and discuss the respective model parameters. Due to the representations of the coverages in terms of the applied potential we provide an adsorption map and introduce adsorption potentials. Finally we investigate the structure of the space charge layer at the metal/surface/electrolyte interface by means of numerical solutions of the coupled Poisson-momentum equation system for various applied potentials. It turns out that various layers self-consistently form within the overall space charge region, which are compared to historic and recent pictures of the double layer. Based on this we present new interpretations of what is known as inner and outer Helmholtz-planes and finally provide a thermodynamic consistent picture of the metal/electrolyte interface structure.

  • J. Fuhrmann, A numerical strategy for Nernst--Planck systems with solvation effect, Fuel Cells, 16 (2016), pp. 704--714.

  • J. Fuhrmann, A. Linke, Ch. Merdon, F. Neumann, T. Streckenbach, H. Baltruschat, M. Khodayari, Inverse modeling of thin layer flow cells for detection of solubility, transport and reaction coefficients from experimental data, Electrochimica Acta, 211 (2016), pp. 1--10.
    Abstract
    Thin layer flow cells are used in electrochemical research as experimental devices which allow to perform investigations of electrocatalytic surface reactions under controlled conditions using reasonably small electrolyte volumes. The paper introduces a general approach to simulate the complete cell using accurate numerical simulation of the coupled flow, transport and reaction processes in a flow cell. The approach is based on a mass conservative coupling of a divergence-free finite element method for fluid flow and a stable finite volume method for mass transport. It allows to perform stable and efficient forward simulations that comply with the physical bounds namely mass conservation and maximum principles for the involved species. In this context, several recent approaches to obtain divergence-free velocities from finite element simulations are discussed. In order to perform parameter identification, the forward simulation method is coupled to standard optimization tools. After an assessment of the inverse modeling approach using known realistic data, first results of the identification of solubility and transport data for O2 dissolved in organic electrolytes are presented. A plausibility study for a more complex situation with surface reactions concludes the paper and shows possible extensions of the scope of the presented numerical tools.

  • A. Linke, Ch. Merdon, On velocity errors due to irrotational forces in the Navier--Stokes momentum balance, Journal of Computational Physics, 313 (2016), pp. 654--661.
    Abstract
    This contribution studies the influence of the pressure on the velocity error in finite element discretisations of the Navier--Stokes equations. Three simple benchmark problems that are all close to real-world applications convey that the pressure can be comparably large and is not to be underestimated. For widely used finite element methods like the Taylor--Hood finite element method, such relatively large pressures can lead to spurious oscillations and arbitrarily large errors in the velocity, even if the exact velocity is in the ansatz space. Only mixed finite element methods, whose velocity error is pressure-independent, like the Scott--Vogelius finite element method can avoid this influence.

  • A. Linke, Ch. Merdon, Pressure-robustness and discrete Helmholtz projectors in mixed finite element methods for the incompressible Navier--Stokes equations, Computer Methods in Applied Mechanics and Engineering, 311 (2016), pp. 304--326.
    Abstract
    Recently, it was understood how to repair a certain L2-orthogonality of discretely-divergence-free vector fields and gradient fields such that the velocity error of inf-sup stable discretizations for the incompressible Stokes equations becomes pressure-independent. These new 'pressure-robust' Stokes discretizations deliver a small velocity error, whenever the continuous velocity field can be well approximated on a given grid. On the contrary, classical inf-sup stable Stokes discretizations can guarantee a small velocity error only, when both the velocity and the pressure field can be approximated well, simultaneously.
    In this contribution, 'pressure-robustness' is extended to the time-dependent Navier--Stokes equations. In particular, steady and time-dependent potential flows are shown to build an entire class of benchmarks, where pressure-robust discretizations can outperform classical approaches significantly. Speedups will be explained by a new theoretical concept, the 'discrete Helmholtz projector' of an inf-sup stable discretization. Moreover, different discrete nonlinear convection terms are discussed, and skew-symmetric pressure-robust discretizations are proposed.

  • P.-É. Druet, Some mathematical problems related to the second order optimal shape of a crystallization interface, Discrete and Continuous Dynamical Systems, 35 (2015), pp. 2443--2463.
    Abstract
    We consider the problem to optimize the stationary temperature distribution and the equilibrium shape of the solid-liquid interface in a two-phase system subject to a temperature gradient. The interface satisfies the minimization principle of the free energy, while the temperature is solving the heat equation with a radiation boundary conditions at the outer wall. Under the condition that the temperature gradient is uniformly negative in the direction of crystallization, the interface is expected to have a global graph representation. We reformulate this condition as a pointwise constraint on the gradient of the state, and we derive the first order optimality system for a class of objective functionals that account for the second surface derivatives, and for the surface temperature gradient.

  • M. Liero, Th. Koprucki, A. Fischer, R. Scholz, A. Glitzky, p-Laplace thermistor modeling of electrothermal feedback in organic semiconductors, ZAMP Zeitschrift fur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Mathematiques et de Physique Appliquees, 66 (2015), pp. 2957--2977.
    Abstract
    In large-area Organic Light-Emitting Diodes (OLEDs) spatially inhomogeneous luminance at high power due to inhomogeneous current flow and electrothermal feedback can be observed. To describe these self-heating effects in organic semiconductors we present a stationary thermistor model based on the heat equation for the temperature coupled to a p-Laplace-type equation for the electrostatic potential with mixed boundary conditions. The p-Laplacian describes the non-Ohmic electrical behavior of the organic material. Moreover, an Arrhenius-like temperature dependency of the electrical conductivity is considered. We introduce a finite-volume scheme for the system and discuss its relation to recent network models for OLEDs. In two spatial dimensions we derive a priori estimates for the temperature and the electrostatic potential and prove the existence of a weak solution by Schauder's fixed point theorem.

  • E. Meca Álvarez, I. Mercader, L. Ramirez-Piscina, Transitions between symmetric and nonsymmetric regimes in binary-mixture convection, Physica D. Nonlinear Phenomena, 303 (2015), pp. 39--49.

  • D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, K. Gärtner, M. Virgilio, S. Guha, G. Capellini, Th. Koprucki, Th. Schröder, Modeling of edge-emitting lasers based on tensile strained germanium microstrips, IEEE Photonics Journal, 7 (2015), pp. 1502115/1--1502115/15, DOI 10.1109/JPHOT.2015.2427093 .
    Abstract
    In this paper we present a thorough modeling of an edge-emitting laser based on strained germanium microstrips. The full band structure of the tensile strained germanium (Ge) layer enters the calculation of optical properties. Material gain for strained Ge is used in the two-dimensional simulation of the carrier transport and of the optical field within a cross section of the microstrips orthogonal to the optical cavity. We study optoelectronic properties of the device for two different designs. The simulation results are very promising as they show feasible ways towards Ge emitter devices with lower threshold currents and higher efficiency as published insofar.

  • M. Radszuweit, E. Alvarez-Lacalle, M. Bär, B. Echebarria, Cardiac contraction induces discordant alternans and localized block, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 91 (2015), pp. 022703/1--022703/12.
    Abstract
    In this paper we use a simplified model of cardiac excitation-contraction coupling to study the effect of tissue deformation on the dynamics of alternans, i.e. alternations in the duration of the cardiac action potential, that occur at fast pacing rates and are known to be pro-arrhythmic. We show that small stretch-activated currents can produce large effects and cause a transition from in-phase to off-phase alternations (i.e. from concordant to discordant alternans) and to conduction blocks. We demonstrate numerically and analytically that this effect is the result of a generic change in the slope of the conduction velocity restitution curve due to electromechanical coupling. Thus, excitation-contraction coupling can potentially play a relevant role in the transition to reentry and fibrillation.

  • CH. Brennecke, A. Linke, Ch. Merdon, J. Schöberl, Optimal and pressure-independent $L^2$ velocity error estimates for a modified Crouzeix--Raviart Stokes element with BDM reconstructions, Journal of Computational Mathematics, 33 (2015), pp. 191--208.
    Abstract
    Nearly all inf-sup stable mixed finite elements for the incompressible Stokes equations relax the divergence constraint. The price to pay is that a priori estimates for the velocity error become pressure-dependent, while divergence-free mixed finite elements deliver pressure-independent estimates. A recently introduced new variational crime using lowest-order Raviart-Thomas velocity reconstructions delivers a much more robust modified Crouzeix-Raviart element, obeying an optimal pressure-independent discrete H1 velocity estimate. Refining this approach, a more sophisticated variational crime employing the lowest-order BDM element is proposed, which also allows proving an optimal pressure independent L2 velocity error. Numerical examples confirm the analysis and demonstrate the improved robustness in the Navier-Stokes case.

  • W. Huang, L. Kamenski, R.D. Russell, A comparative numerical study of meshing functionals for variational mesh adaptation, Journal of Mathematical Study, 48 (2015), pp. 168--186.
    Abstract
    We present a comparative numerical study for three functionals used for variational mesh adaptation. One of them is a generalization of Winslow's variable diffusion functional while the others are based on equidistribution and alignment. These functionals are known to have nice theoretical properties and work well for most mesh adaptation problems either as a stand-alone variational method or combined within the moving mesh framework. Their performance is investigated numerically in terms of equidistribution and alignment mesh quality measures. Numerical results in 2D and 3D are presented.

  • W. Huang, L. Kamenski, A geometric discretization and a simple implementation for variational mesh generation and adaptation, Journal of Computational Physics, 301 (2015), pp. 322--337.
    Abstract
    We present a simple direct discretization for functionals used in the variational mesh generation and adaptation. Meshing functionals are discretized on simplicial meshes and the Jacobian matrix of the continuous coordinate transformation is approximated by the Jacobian matrices of affine mappings between elements. The advantage of this direct geometric discretization is that it preserves the basic geometric structure of the continuous functional, which is useful in preventing strong decoupling or loss of integral constraints satisfied by the functional. Moreover, the discretized functional is a function of the coordinates of mesh vertices and its derivatives have a simple analytical form, which allows a simple implementation of variational mesh generation and adaptation on computer. Since the variational mesh adaptation is the base for a number of adaptive moving mesh and mesh smoothing methods, the result in this work can be used to develop simple implementations of those methods. Numerical examples are given.

  • R. Huth, S. Jachalski, G. Kitavtsev, D. Peschka, Gradient flow perspective on thin-film bilayer flows, Journal of Engineering Mathematics, 94 (2015), pp. 43--61.
    Abstract
    We study gradient flow formulations of thin-film bilayer flows with triple-junctions between liquid/liquid/air. First we highlight the gradient structure in the Stokes free-boundary flow and identify its solutions with the well known PDE with boundary conditions. Next we propose a similar gradient formulation for the corresponding thin-film model and formally identify solutions with those of the corresponding free-boundary problem. A robust numerical algorithm for the thin-film gradient flow structure is then provided. Using this algorithm we compare the sharp triple-junction model with precursor models. For their stationary solutions a rigorous connection is established using Gamma-convergence. For time-dependent solutions the comparison of numerical solutions shows a good agreement for small and moderate times. Finally we study spreading in the zero-contact angle case, where we compare numerical solutions with asymptotically exact source-type solutions.

  • T. Roubíček, M. Thomas, Ch. Panagiotopoulos, Stress-driven local-solution approach to quasistatic brittle delamination, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 22 (2015), pp. 645--663.
    Abstract
    A unilateral contact problem between elastic bodies at small strains glued by a brittle adhesive is addressed in the quasistatic rate-independent setting. The delamination process is modelled as governed by stresses rather than by energies. This results in a specific scaling of an approximating elastic adhesive contact problem, discretised by a semi-implicit scheme and regularized by a BV-type gradient term. An analytical zero-dimensional example motivates the model and a specific local-solution concept. Two-dimensional numerical simulations performed on an engineering benchmark problem of debonding a fiber in an elastic matrix further illustrate the validity of the model, convergence, and algorithmical efficiency even for very rigid adhesives with high elastic moduli.

  • N. Ahmed, G. Matthies, Higher order continuous Galerkin--Petrov time stepping schemes for transient convection-diffusion-reaction equations, ESAIM: Mathematical Modelling and Numerical Analysis, 49 (2015), pp. 1429--1450.
    Abstract
    We present the analysis for the higher order continuous Galerkin--Petrov (cGP) time discretization schemes in combination with the one-level local projection stabilization in space applied to time-dependent convection-diffusion-reaction problems. Optimal a-priori error estimates will be proved. Numerical studies support the theoretical results. Furthermore, a numerical comparison between continuous Galerkin--Petrov and discontinuous Galerkin time discretization schemes will be given.

  • N. Ahmed, V. John, Adaptive time step control for higher order variational time discretizations applied to convection-diffusion equations, Computer Methods in Applied Mechanics and Engineering, 285 (2015), pp. 83--101.
    Abstract
    Higher order variational time stepping schemes allow an efficient post-processing for computing a higher order solution. This paper presents an adaptive algorithm whose time step control utilizes the post-processed solution. The algorithm is applied to convection-dominated convection-diffusion equations. It is shown that the length of the time step properly reflects the dynamics of the solution. The numerical costs of the adaptive algorithm are discussed.

  • A. Caiazzo, G. Montecinos, L.O. Müller, E.M. Haacke, E.F. Toro, Computational haemodynamics in stenotic internal jugular veins, Journal of Mathematical Biology, 70 (2015), pp. 745--772.
    Abstract
    Stenosis in internal jugular veins (IJVs) are frequently associated to pathological venous circulation and insufficient cerebral blood drainage. In this work, we set up a computational framework to assess the relevance of IJV stenoses through numerical simulation, combining medical imaging, patient-specific data and a mathematical model for venous occlusions. Coupling a three-dimensional (3D) description of blood flow in IJVs with a reduced one-dimesional model (1D) for major intracranial veins, we are able to model different anatomical configurations, an aspect of importance to understand the impact of IJV stenosis in intracranial venous haemodynamics. We investigate several stenotic configurations in a physiologic patient-specific regime, quantifying the effect of the stenosis in terms of venous pressure increase and wall shear stress patterns. Simulation results are in qualitative agreement with reported pressure anomalies in pathological cases. Moreover, they demonstrate the potential of the proposed multiscale framework for individual-based studies and computer-aided diagnosis.

  • J. Fuhrmann, Comparison and numerical treatment of generalized Nernst--Planck models, Computer Physics Communications. An International Journal and Program Library for Computational Physics and Physical Chemistry, 196 (2015), pp. 166--178.
    Abstract
    In its most widespread, classical formulation, the Nernst-Planck-Poisson system for ion transport in electrolytes fails to take into account finite ion sizes. As a consequence, it predicts unphysically high ion concentrations near electrode surfaces. Historical and recent approaches to an approriate modification of the model are able to fix this problem. Several appropriate formulations are compared in this paper. The resulting equations are reformulated using absolute activities as basic variables describing the species amounts. This reformulation allows to introduce a straightforward generalisation of the Scharfetter-Gummel finite volume discretization scheme for drift-diffusion equations. It is shown that it is thermodynamically consistent in the sense that the solution of the corresponding discretized generalized Poisson-Boltzmann system describing the thermodynamic equilibrium is a stationary state of the discretized time-dependent generalized Nernst-Planck system. Numerical examples demonstrate the improved physical correctness of the generalised models and the feasibility of the numerical approach.

  • CH. Heinemann, Ch. Kraus, Existence of weak solutions for a PDE system describing phase separation and damage processes including inertial effects, Discrete and Continuous Dynamical Systems, 35 (2015), pp. 2565--2590.
    Abstract
    In this paper, we consider a coupled PDE system describing phase separation and damage phenomena in elastically stressed alloys in the presence of inertial effects. The material is considered on a bounded Lipschitz domain with mixed boundary conditions for the displacement variable. The main aim of this work is to establish existence of weak solutions for the introduced hyperbolic-parabolic system. To this end, we first generalize the notion of weak solution introduced in WIAS 1520. Then we prove existence of weak solutions by means of regularization, time-discretization and different variational techniques.

  • CH. Heinemann, E. Rocca, Damage processes in thermoviscoelastic materials with damage-dependent thermal expansion coefficients, Mathematical Methods in the Applied Sciences, 38 (2015), pp. 4587--4612.
    Abstract
    In this paper we prove existence of global in time weak solutions for a highly nonlinear PDE system arising in the context of damage phenomena in thermoviscoelastic materials. The main novelty of the present contribution with respect to the ones already present in the literature consists in the possibility of taking into account a damage-dependent thermal expansion coefficient. This term implies the presence of nonlinear couplings in the PDE system, which make the analysis more challenging.

  • A. Linke, Ch. Merdon, Guaranteed energy error estimators for a modified robust Crouzeix--Raviart Stokes element, Journal of Scientific Computing, 64 (2015), pp. 541--558.
    Abstract
    This paper provides guaranteed upper energy error bounds for a modified lowest-order nonconforming Crouzeix--Raviart finite element method for the Stokes equations. The modification from [A. Linke 2014, On the role of the Helmholtz-decomposition in mixed methods for incompressible flows and a new variational crime] is based on the observation that only the divergence-free part of the right-hand side should balance the vector Laplacian. The new method has optimal energy error estimates and can lead to errors that are smaller by several magnitudes, since the estimates are pressure-independent. An efficient a posteriori velocity error estimator for the modified method also should involve only the divergence-free part of the right-hand side. Some designs to approximate the Helmholtz projector are compared and verified by numerical benchmark examples. They show that guaranteed error control for the modified method is possible and almost as sharp as for the unmodified method.

  • A. Mielke, J. Naumann, Global-in-time existence of weak solutions to Kolmogorov's two-equation model of turbulence, Comptes Rendus Mathematique. Academie des Sciences. Paris, 353 (2015), pp. 321--326.
    Abstract
    We consider Kolmogorov's model for the turbulent motion of an incompressible fluid in ℝ3. This model consists in a Navier-Stokes type system for the mean flow u and two further partial differential equations: an equation for the frequency ω and for the kinetic energy k each. We investigate this system of partial differential equations in a cylinder Ω x ]0,T[ (Ω ⊂ ℝ3 cube, 0 < T < +∞) under spatial periodic boundary conditions on ∂Ω x ]0,T[ and initial conditions in Ω x {0}. We present an existence result for a weak solution {u, ω, k} to the problem under consideration, with ω, k obeying the inequalities formula1 and formula2.

  • R.M. Arkhipov, I. Babushkin, M.K. Lebedev, Y.A. Tolmachev, M.V. Arkhipov, Transient Cherenkov radiation from an inhomogeneous string excited by an ultrashort laser pulse at superluminal velocity, Physical Review A, 89 (2014), pp. 043811/1--043811/10.
    Abstract
    An optical response of one-dimensional string made of dipoles with a periodically varying density excited by a spot of light moving along the string at the superluminal (subluminal) velocity is studied. We consider in details the spectral and temporal dynamics of the Cherenkov radiation, which occurs in such system in the transient regime. We point out the resonance character of radiation and the appearance of a new Doppler-like frequency in the spectrum of the transient Cherenkov radiation. Possible applications of the effect as well as different string topologies are discussed

  • A. Linke, On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime, Computer Methods in Applied Mechanics and Engineering, 268 (2014), pp. 782--800.
    Abstract
    According to the Helmholtz decomposition, the irrotational parts of the momentum balance equations of the incompressible Navier-Stokes equations are balanced by the pressure gradient. Unfortunately, nearly all mixed methods for incompressible flows violate this fundamental property, resulting in the well-known numerical instability of poor mass conservation. The origin of this problem is the lack of L2-orthogonality between discretely divergence-free velocities and irrotational vector fields. In order to cure this, a new variational crime using divergence-free velocity reconstructions is proposed. Applying lowest order Raviart-Thomas velocity reconstructions to the nonconforming Crouzeix-Raviart element allows to construct a cheap flow discretization for general 2d and 3d simplex meshes that possesses the same advantageous robustness properties like divergence-free flow solvers. In the Stokes case, optimal a-priori error estimates for the velocity gradients and the pressure are derived. Moreover, the discrete velocity is independent of the continuous pressure. Several detailed linear and nonlinear numerical examples illustrate the theoretical findings.

  • E. Jenkins, V. John, A. Linke, L.G. Rebholz, On the parameter choice in grad-div stabilization for the Stokes equations, Advances in Computational Mathematics, 40 (2014), pp. 491--516.
    Abstract
    Grad-div stabilization has been proved to be a very useful tool in discretizations of incompressible flow problems. Standard error analysis for inf-sup stable conforming pairs of finite element spaces predicts that the stabilization parameter should be optimally chosen to be O(1). This paper revisits this choice for the Stokes equations on the basis of minimizing the $H^1$ error of the velocity and the $L^2$ error of the pressure. It turns out, by applying a refined error analysis, that the optimal parameter choice is more subtle than known so far in the literature. It depends on the used norm, the solution, the family of finite element spaces, and the type of mesh. Depending on the situation, the optimal stabilization parameter might range from being very small to very large. The analytic results are supported by numerical examples.

  • R. Eymard, J. Fuhrmann, A. Linke, On MAC schemes on triangular Delaunay meshes, their convergence and application to coupled flow problems, Numerical Methods for Partial Differential Equations. An International Journal, 30 (2014), pp. 1397--1424.
    Abstract
    We study two classical generalized MAC schemes on unstructured triangular Delaunay meshes for the incompressible Stokes and Navier-Stokes equations and prove their convergence for the first time. These generalizations use the duality between Voronoi and triangles of Delaunay meshes, in order to construct two staggered discretization schemes. Both schemes are especially interesting, since compatible finite volume discretizations for coupled convection-diffusion equations can be constructed which preserve discrete maximum principles. In the first scheme, called tangential velocity scheme, the pressures are defined at the vertices of the mesh, and the discrete velocities are tangential to the edges of the triangles. In the second scheme, called normal velocity scheme, the pressures are defined in the triangles, and the discrete velocities are normal to the edges of the triangles. For both schemes, we prove the convergence in $L^2$ for the velocities and the discrete rotations of the velocities for the Stokes and the Navier-Stokes problem. Further, for the normal velocity scheme, we also prove the strong convergence of the pressure in $L^2$. Linear and nonlinear numerical examples illustrate the theoretical predictions.

  • A. Fiebach, A. Glitzky, A. Linke, Uniform global bounds for solutions of an implicit Voronoi finite volume method for reaction-diffusion problems, Numerische Mathematik, 128 (2014), pp. 31--72.
    Abstract
    We consider discretizations for reaction-diffusion systems with nonlinear diffusion in two space dimensions. The applied model allows to handle heterogeneous materials and uses the chemical potentials of the involved species as primary variables. We propose an implicit Voronoi finite volume discretization on regular Delaunay meshes that allows to prove uniform, mesh-independent global upper and lower $L^infty$ bounds for the chemical potentials. These bounds provide the main step for a convergence analysis for the full discretized nonlinear evolution problem. The fundamental ideas are energy estimates, a discrete Moser iteration and the use of discrete Gagliardo-Nirenberg inequalities. For the proof of the Gagliardo-Nirenberg inequalities we exploit that the discrete Voronoi finite volume gradient norm in $2d$ coincides with the gradient norm of continuous piecewise linear finite elements.

  • A. Gloria, S. Neukamm, F. Otto, An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations, ESAIM: Mathematical Modelling and Numerical Analysis, 48 (2014), pp. 325--346.
    Abstract
    We establish an optimal, linear rate of convergence for the stochastic homogenization of discrete linear elliptic equations. We consider the model problem of independent and identically distributed coefficients on a discretized unit torus. We show that the difference between the solution to the random problem on the discretized torus and the first two terms of the two-scale asymptotic expansion has the same scaling as in the periodic case. In particular the L2-norm in probability of the H1-norm in space of this error scales like ε, where ε is the discretization parameter of the unit torus. The proof makes extensive use of previous results by the authors, and of recent annealed estimates on the Greens function by Marahrens and the third author.

  • R. Guibert, K. Mcleod, A. Caiazzo, T. Mansi, Group-wise construction of reduced models for understanding and characterization of pulmonary blood flows from medical images, Medical Image Analysis, 18 (2014), pp. 63--82.

  • A. Caiazzo, V. John, U. Wilbrandt, On classical iterative subdomain methods for the Stokes--Darcy problem, Computer & Geosciences, 18 (2014), pp. 711--728.
    Abstract
    Iterative subdomain methods for the Stokes--Darcy problem that use Robin boundary conditions on the interface are reviewed. Their common underlying structure and their main differences are identified. In particular, it is clarified that there are different updating strategies for the interface conditions. For small values of fluid viscosity and hydraulic permeability, which are relevant in applications from geosciences, it is shown in numerical studies that only one of these updating strategies leads to an efficient numerical method, if this strategy is used in combination with appropriate parameters in the Robin boundary conditions. In particular, it is observed that the values of appropriate parameters are larger than those proposed so far. Not only the size but also the ratio of appropriate Robin parameters depends on the coefficients of the problem.

  • A. Caiazzo, J. Mura, Multiscale modeling of weakly compressible elastic materials in harmonic regime and application to microscale structure estimation, Multiscale Modeling & Simulation. A SIAM Interdisciplinary Journal, 12 (2014), pp. 514--537.
    Abstract
    This article is devoted to the modeling of elastic materials composed by an incompressible elastic matrix and small compressible gaseous inclusions, under a time harmonic excitation. In a biomedical context, this model describes the dynamics of a biological tissue (e.g. lung or liver) when wave analysis methods (such as Magnetic Resonance Elastography) are used to estimate tissue properties. Due to the multiscale nature of the problem, direct numerical simulations are prohibitive. We extend the homogenized model introduced in [Baffico, Grandmont, Maday, Osses, SIAM J. Mult. Mod. Sim., 7(1), 2008] to a time harmonic regime to describe the solid-gas mixture from a macroscopic point of view in terms of an effective elasticity tensor. Furthermore, we derive and validate numerically analytical approximations for the effective elastic coefficients in terms of macroscopic parameters. This simplified description is used to to set up an efficient variational approach for the estimation of the tissue porosity, using the mechanical response to external harmonic excitations.

  • L. Kamenski, W. Huang, A study on the conditioning of finite element equations with arbitrary anisotropic meshes via a density function approach, Journal of Mathematical Study, 47 (2014), pp. 151--172.

  • L. Kamenski, W. Huang, How a nonconvergent recovered Hessian works in mesh adaptation, SIAM Journal on Numerical Analysis, 52 (2014), pp. 1692--1708.

  • L. Kamenski, W. Huang, H. Xu, Conditioning of finite element equations with arbitrary anisotropic meshes, Mathematics of Computation, 83 (2014), pp. 2187--2211.

  • A. Pérez-Serrano, J. Javaloyes, S. Balle, Directional reversals and multimode dynamics in semiconductor ring lasers, Physical Review A, 89 (2014), pp. 023818/1--023818/14.
    Abstract
    We investigate the dynamics of longitudinal modes in quantum-well semiconductor ring lasers by means of a spatio-temporal travelling wave model. We report the existence of a novel multimode instability in such a system that provokes a periodic deterministic directional reversal involving jumps between consecutive longitudinal modes. The switching sequence follows the modal frequencies from blue to red, and every modal jump is accompanied by a reversal of the direction of emission. We characterize and analyze such instability via the bifurcation analysis of the full travelling wave model as well as by performing the linear stability analysis of the monochromatic solutions.

  • K. Götze, Strong solutions for the interaction of a rigid body and a viscoelastic fluid, Journal of Mathematical Fluid Mechanics, 15 (2013), pp. 663--688.
    Abstract
    We study a coupled system of equations describing the movement of a rigid body which is immersed in a viscoelastic fluid. It is shown that under natural assumptions on the data and for general goemetries of the rigid body, excluding contact scenarios, a unique local-in-time strong solution exists.

  • M. Liero, A. Mielke, Gradient structures and geodesic convexity for reaction-diffusion systems, Philosophical Transactions of the Royal Society A : Mathematical, Physical & Engineering Sciences, 371 (2013), pp. 20120346/1--20120346/28.
    Abstract
    We consider systems of reaction-diffusion equations as gradient systems with respect to an entropy functional and a dissipation metric given in terms of a so-called Onsager operator, which is a sum of a diffusion part of Wasserstein type and a reaction part. We provide methods for establishing geodesic lambda-convexity of the entropy functional by purely differential methods, thus circumventing arguments from mass transportation. Finally, several examples, including a drift-diffusion system, provide a survey on the applicability of the theory. We consider systems of reaction-diffusion equations as gradient systems with respect to an entropy functional and a dissipation metric given in terms of a so-called Onsager operator, which is a sum of a diffusion part of Wasserstein type and a reaction part. We provide methods for establishing geodesic lambda-convexity of the entropy functional by purely differential methods, thus circumventing arguments from mass transportation. Finally, several examples, including a drift-diffusion system, provide a survey on the applicability of the theory.

  • A. Pérez-Serrano, J. Javaloyes, S. Balle, Multi-channel wavelength conversion using four-wave mixing in semiconductor ring lasers, IEEE Phot. Tech. Letter, 25 (2013), pp. 476--479.
    Abstract
    We theoretically study all-optical simultaneous wavelength conversion of multiple channels by four-wave mixing in semiconductor ring lasers. Locking the semiconductor ring laser to a holding beam allows to achieve large conversion efficiencies with good signal-tonoise ratio in several channels at multi-Gb/s bit rates. Cross-talk between signals, arising from the peculiar four-wave mixing cascade of modes in semiconductor ring lasers and their cross-gain saturation, is studied in detail. We show that it can be controlled by adjusting the intensity of the holding beam, the bias current of the laser and the number, intensity and wavelength of signals that one wants to convert.

  • A. Pérez-Serrano, J. Javaloyes, S. Balle, Spectral delay algebraic equation approach to broad area laser diodes, IEEE J. Select. Topics Quantum Electron., 19 (2013), pp. 1502808/1--1502808/8.

  • M.V. Arkhipov, R.M. Arkhipov, S.A. Pulkin, Effects of inversionless oscillation in two-level media from the point of view of specificities of the spatiotemporal propagation dynamics of radiation, Optics and Spectroscopy, 114 (2013), pp. 831--837.
    Abstract
    We report the results of computer simulation of the emission of radiation by an extended twolevel medium in a ring cavity. The cases of using strong external monochromatic, quasimonochromatic, and biharmonic radiation for pumping the twolevel medium are analyzed. It is shown that the emission of radiation with spectral content different from that of the pump radiation, which is interpreted as the inversionless oscillation, is the result of the spatiotemporal dynamics of light propagation in an extended twolevel medium imbedded in a cavity. The appearance of this radiation is not related to known resonances of amplification of a weak probe field in a thin layer of the twolevel system (the effect of inversionless oscillation) induced by strong resonance monochromatic or biharmonic field, as was thought before.

  • C. Bertoglio, A. Caiazzo, M.A. Fernàndez, Fractional-step schemes for the coupling of distributed and lumped models in hemodynamics, SIAM Journal on Scientific Computing, 35 (2013), pp. B551--B575.

  • A. Bradji, J. Fuhrmann, Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes, Applications of Mathematics, 58 (2013), pp. 1--38.
    Abstract
    A general class of nonconforming meshes has been recently studied for stationary anisotropic heterogeneous diffusion problems by R. Eymard and coworkers. Thanks to these basic ideas developed for stationary problems, we derive a new discretization scheme in order to approximate the nonstationary heat problem. The unknowns of this scheme are the values at the centre of the control volumes, at some internal interfaces, and at the mesh points of the time discretization. Although the numerical scheme stems from the finite volume method, its formulation is based on the discrete version for the weak formulation defined for the heat problem. We derive error estimates for the solution in discrete norm, and an error estimate for an approximation of the gradient, in a general framework in which the discrete bilinear form is satisfying ellipticity. We prove in particular, that, when the discrete flux is calculated using a stabilized discrete gradient, the convergence order is h+k , where h (resp. k) is the mesh size of the spatial (resp. time) discretization. This estimate is valid under the regularity assumption that the exact solution is twice continuously differentiable in time and space. These error estimates are useful because they allow us to get error estimates for the approximations of the exact solution and its first derivatives.

  • B. Cousins, S. Le Borne, A. Linke, Z. Wang, Efficient linear solvers for incompressible flow simulations using Scott--Vogelius finite elements, Numerical Methods for Partial Differential Equations. An International Journal, 29 (2013), pp. 1217--1237.
    Abstract
    Recent research has shown that in some practically relevant situations like multiphysics flows (Galvin et al., Comput Methods Appl Mech Eng, 2012) divergence-free mixed finite elements may have a significantly smaller discretization error than standard nondivergence-free mixed finite elements. To judge the overall performance of divergence-free mixed finite elements, we investigate linear solvers for the saddle point linear systems arising in Scott-Vogelius finite element implementations of the incompressible Navier-Stokes equations. We investigate both direct and iterative solver methods. Due to discontinuous pressure elements in the case of Scott-Vogelius (SV) elements, considerably more solver strategies seem to deliver promising results than in the case of standard mixed finite elements such as Taylor-Hood elements. For direct methods, we extend recent preliminary work using sparse banded solvers on the penalty method formulation to finer meshes and discuss extensions. For iterative methods, we test augmented Lagrangian and H -LU preconditioners with GMRES, on both full and statically condensed systems. Several numerical experiments are provided that show these classes of solvers are well suited for use with SV elements and could deliver an interesting overall performance in several applications.

  • D. Knees, A. Schröder, Computational aspects of quasi-static crack propagation, Discrete and Continuous Dynamical Systems -- Series S, 6 (2013), pp. 63--99.
    Abstract
    The focus of this note lies on the numerical analysis of models describing the propagation of a single crack in a linearly elastic material. The evolution of the crack is modeled as a rate-independent process based on the Griffith criterion. We follow two different approaches for setting up mathematically well defined models: the global energetic approach and an approach based on a viscous regularization. We prove the convergence of solutions of fully discretized models (i.e. with respect to time and space) and derive relations between the discretization parameters (mesh size, time step size, viscosity parameter, crack increment) which guarantee the convergence of the schemes. Further, convergence rates are provided for the approximation of energy release rates by certain discrete energy release rates. Thereby we discuss both, models with self-contact conditions on the crack faces as well as models with pure Neumann conditions on the crack faces. The convergence proofs rely on regularity estimates for the elastic fields close to the crack tip and local and global finite element error estimates. Finally the theoretical results are illustrated with some numerical calculations.

  • W. Dreyer, C. Guhlke, R. Müller, Overcoming the shortcomings of the Nernst--Planck model, Physical Chemistry Chemical Physics, 15 (2013), pp. 7075--7086.
    Abstract
    This is a study on electrolytes that takes a thermodynamically consistent coupling between mechanics and diffusion into account. It removes some inherent deficiencies of the popular Nernst-Planck model. A boundary problem for equilibrium processes is used to illustrate the new features of our model.

  • A. Linke, L. Rebholz, On a reduced sparsity stabilization of grad-div type for incompressible flow problems, Computer Methods in Applied Mechanics and Engineering, 261--262 (2013), pp. 142--153.
    Abstract
    We introduce a new operator for stabilizing error that arises from the weak enforcement of mass conservation in finite element simulations of incompressible flow problems. We show this new operator has a similar positive effect on velocity error as the well-known and very successful grad-div stabilization operator, but the new operator is more attractive from an implementation standpoint because it yields a sparser block structure matrix. That is, while grad-div produces fully coupled block matrices (i.e. block-full), the matrices arising from the new operator are block-upper triangular in two dimensions, and in three dimensions the 2,1 and 3,1 blocks are empty. Moreover, the diagonal blocks of the new operator's matrices are identical to those of grad-div. We provide error estimates and numerical examples for finite element simulations with the new operator, which reveals the significant improvement in accuracy it can provide. Solutions found using the new operator are also compared to those using usual grad-div stabilization, and in all cases, solutions are found to be very similar.

  • A. Mielke, R. Rossi, G. Savaré, Nonsmooth analysis of doubly nonlinear evolution equations, Calculus of Variations and Partial Differential Equations, 46 (2013), pp. 253--310.
    Abstract
    In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general sufficient conditions, on the dissipation potential and the energy functional, for existence of solutions to the related Cauchy problem. We prove our main existence result by passing to the limit in a time-discretization scheme with variational techniques. Finally, we discuss an application to a material model in finite-strain elasticity.

  • A. Mielke, E. Rohan, Homogenization of elastic waves in fluid-saturated porous media using the Biot model, Mathematical Models & Methods in Applied Sciences, 23 (2013), pp. 873--916.
    Abstract
    We consider periodically heterogeneous fluid-saturated poroelastic media described by the Biot model with inertia effects. The weak and semistrong formulations for displacement, seepage and pressure fields involve three equations expressing the momentum and mass balance and the Darcy law. Using the two-scale homogenization method we obtain the limit two-scale problem and prove the existence and uniqueness of its weak solutions. The Laplace transformation in time is used to decouple the macroscopic and microscopic scales. It is shown that the seepage velocity is eliminated form the macroscopic equations involving strain and pressure fields only. The plane harmonic wave propagation is studied using an example of layered medium. Illustrations show some influence of the orthotropy on the dispersion phenomena.

  • P.N. Racec, S. Schade, H.-Chr. Kaiser, Eigensolutions of the Wigner--Eisenbud problem for a cylindrical nanowire within finite volume method, Journal of Computational Physics, 252 (2013), pp. 52--64.
    Abstract
    We present a finite volume method for computing a representative range of eigenvalues and eigenvectors of the Schrödinger operator on a three dimensional cylindrically symmetric bounded domain with mixed boundary conditions. More specifically, we deal with a semiconductor nanowire which consists of a dominant host material and contains heterostructure features such as double-barriers or quantum dots. The three dimensional Schrödinger operator is reduced to a family of two dimensional Schrödinger operators distinguished by a centrifugal potential. Ultimately, we numerically treat them by means of a finite volume method. We consider a uniform, boundary conforming Delaunay mesh, which additionally conforms to the material interfaces. The 1/r singularity is eliminated by approximating r at the vertexes of the Voronoi boxes. We study how the anisotropy of the effective mass tensor acts on the uniform approximation of the first K eigenvalues and eigenvectors and their sequential arrangement. There exists an optimal uniform Delaunay discretization with matching anisotropy. This anisotropic discretization yields best accuracy also in the presence of a mildly varying scattering potential, shown exemplarily for a nanowire resonant tunneling diode. For potentials with 1/r singularity one retrieves the theoretically established first order convergence, while the second order convergence is recovered only on uniform grids with an anisotropy correction.

  • S. Amiranashvili, U. Bandelow, A. Mielke, Calculation of ultrashort pulse propagation based on rational approximations for medium dispersion, Optical and Quantum Electronics, 44 (2012), pp. 241--246.
    Abstract
    Ultrashort optical pulses contain only a fewoptical cycles and exhibit broad spectra. Their carrier frequency is therefore not well defined and their description in terms of the standard slowly varying envelope approximation becomes questionable. Existing modeling approaches can be divided in two classes, namely generalized envelope equations, that stem from the nonlinear Schrödinger equation, and non-envelope equations which treat the field directly. Based on fundamental physical rules we will present an approach that effectively interpolates between these classes and provides a suitable setting for accurate and highly efficient

  • K. Galvin, A. Linke, L. Rebholz, N. Wilson, Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection, Computer Methods in Applied Mechanics and Engineering, 237--240 (2012), pp. 166--176.
    Abstract
    We consider the problem of poor mass conservation in mixed finite element algorithms for flow problems with large rotation-free forcing in the momentum equation. We provide analysis that suggests for such problems, obtaining accurate solutions necessitates either the use of pointwise divergence-free finite elements (such as Scott-Vogelius), or heavy grad-div stabilization of weakly divergence-free elements. The theory is demonstrated in numerical experiments for a benchmark natural convection problem, where large irrotational forcing occurs with high Rayleigh numbers.

  • K. Hackl, S. Heinz, A. Mielke, A model for the evolution of laminates in finite-strain elastoplasticity, ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik, 92 (2012), pp. 888--909.
    Abstract
    We study the time evolution in elastoplasticity within the rate-independent framework of generalized standard materials. Our particular interest is the formation and the evolution of microstructure. Providing models where existence proofs are possible is a challenging task since the presence of microstructure comes along with a lack of convexity and, hence, compactness arguments cannot be applied to prove the existence of solutions. In order to overcome this problem, we will incorporate information on the microstructure into the internal variable, which is still compatible with generalized standard materials. More precisely, we shall allow for such microstructure that is given by simple or sequential laminates. We will consider a model for the evolution of these laminates and we will prove a theorem on the existence of solutions to any finite sequence of time-incremental minimization problems. In order to illustrate the mechanical consequences of the theory developed some numerical results, especially dealing with the rotation of laminates, are presented.

  • A. Glitzky, An electronic model for solar cells including active interfaces and energy resolved defect densities, SIAM Journal on Mathematical Analysis, 44 (2012), pp. 3874--3900.
    Abstract
    We introduce an electronic model for solar cells taking into account heterostructures with active interfaces and energy resolved volume and interface trap densities. The model consists of continuity equations for electrons and holes with thermionic emission transfer conditions at the interface and of ODEs for the trap densities with energy level and spatial position as parameters, where the right hand sides contain generation-recombination as well as ionization reactions. This system is coupled with a Poisson equation for the electrostatic potential. We show the thermodynamic correctness of the model and prove a priori estimates for the solutions to the evolution system. Moreover, existence and uniqueness of weak solutions of the problem are proven. For this purpose we solve a regularized problem and verify bounds of the corresponding solution not depending on the regularization level.

  • D. Knees, A. Schröder, Global spatial regularity for elasticity models with cracks, contact and other nonsmooth constraints, Mathematical Methods in the Applied Sciences, 35 (2012), pp. 1859--1884.
    Abstract
    A global higher differentiability result in Besov spaces is proved for the displacement fields of linear elastic models with self contact. Domains with cracks are studied, where nonpenetration conditions/Signorini conditions are imposed on the crack faces. It is shown that in a neighborhood of crack tips (in 2D) or crack fronts (3D) the displacement fields are B 3/2 2,∞ regular. The proof relies on a difference quotient argument for the directions tangential to the crack. In order to obtain the regularity estimates also in the normal direction, an argument due to Ebmeyer/Frehse/Kassmann is modified. The methods are then applied to further examples like contact problems with nonsmooth rigid foundations, to a model with Tresca friction and to minimization problems with nonsmooth energies and constraints as they occur for instance in the modeling of shape memory alloys. Based on Falk's approximation Theorem for variational inequalities, convergence rates for FE-discretizations of contact problems are derived relying on the proven regularity properties. Several numerical examples illustrate the theoretical results.

  • A. Linke, L.G. Rebholz, N.E. Wilson, On the convergence rate of grad-div stabilized Taylor--Hood to Scott--Vogelius solutions for incompressible flow problems, Journal of Mathematical Analysis and Applications, 381 (2011), pp. 612--626.
    Abstract
    It was recently proven that, under mild restrictions, grad-div stabilized Taylor-Hood solutions of Navier-Stokes problems converge to the Scott-Vogelius solution of that same problem. However, even though the analytical rate was only shown to be $gamma^-frac12$ (where $gamma$ is the stabilization parameter), the computational results suggest the rate may be improvable $gamma^-1$. We prove herein the analytical rate is indeed $gamma^-1$, and extend the result to other incompressible flow problems including Leray-$alpha$ and MHD. Numerical results are given that verify the theory.

  • A.G. Vladimirov, R. Lefever, M. Tlidi, Relative stability of multipeak localized patterns of cavity solitons, Physical Review A, 84 (2011), pp. 043848/1--043848/4.
    Abstract
    We study the relative stability of different one-dimensional (1D) and two-dimensional (2D) clusters of closely packed localized peaks of the Swift-Hohenberg equation. In the 1D case, we demonstrate numerically the existence of a spatial Maxwell transition point where all clusters involving up to 15 peaks are equally stable. Above (below) this point, clusters become more (less) stable when their number of peaks increases. In the 2D case, since clusters involving more than two peaks may exhibit distinct spatial arrangements, this point splits into a set of Maxwell transition pointsWe study the relative stability of different one-dimensional (1D) and two-dimensional (2D) clusters of closely packed localized peaks of the Swift-Hohenberg equation. In the 1D case, we demonstrate numerically the existence of a spatial Maxwell transition point where all clusters involving up to 15 peaks are equally stable. Above (below) this point, clusters become more (less) stable when their number of peaks increases. In the 2D case, since clusters involving more than two peaks may exhibit distinct spatial arrangements, this point splits into a set of Maxwell transition points

  • M. Augustin, A. Caiazzo, A. Fiebach, J. Fuhrmann, V. John, A. Linke, R. Umla, An assessment of discretizations for convection-dominated convection-diffusion equations, Computer Methods in Applied Mechanics and Engineering, 200 (2011), pp. 3395--3409.
    Abstract
    The performance of several numerical schemes for discretizing convection-dominated convection-diffusion equations will be investigated with respect to accuracy and efficiency. Accuracy is considered in measures which are of interest in applications. The study includes an exponentially fitted finite volume scheme, the Streamline-Upwind Petrov--Galerkin (SUPG) finite element method, a spurious oscillations at layers diminishing (SOLD) finite element method, a finite element method with continuous interior penalty (CIP) stabilization, a discontinuous Galerkin (DG) finite element method, and a total variation diminishing finite element method (FEMTVD). A detailed assessment of the schemes based on the Hemker example will be presented.

  • M. Case, V. Ervin, A. Linke, L. Rebholz, A connection between Scott--Vogelius and grad-div stabilized Taylor--Hood FE approximations of the Navier--Stokes equations, SIAM Journal on Numerical Analysis, 49 (2011), pp. 1461--1481.
    Abstract
    This article studies two methods for obtaining excellent mass conservation in finite element computations of the Navier-Stokes equations using continuous velocity fields. Under mild restrictions, the Scott-Vogelius element pair has recently been shown to be inf-sup stable and have optimal approximation properties, while also providing pointwise mass conservation. We present herein the first numerical tests of this element pair for the time dependent Navier-Stokes equations. We also prove that, again under these mild restrictions, the limit of the grad-div stabilized Taylor-Hood solutions to the Navier-Stokes problem converges to the Scott-Vogelius solution as the stabilization parameter tends to infinity. That is, in this setting, we provide theoretical justification that choosing the parameter large does not destroy the solution. A limiting result is also proven for the general case. Numerical tests are provided which verify the theory, and show how both Scott-Vogelius and grad-div stabilized Taylor-Hood (with large stabilization parameter) elements can provide accurate results with excellent mass conservation for Navier-Stokes approximations.

  • A. Glitzky, Uniform exponential decay of the free energy for Voronoi finite volume discretized reaction-diffusion systems, Mathematische Nachrichten, 284 (2011), pp. 2159--2174.
    Abstract
    Our focus are energy estimates for discretized reaction-diffusion systems for a finite number of species. We introduce a discretization scheme (Voronoi finite volume in space and fully implicit in time) which has the special property that it preserves the main features of the continuous systems, namely positivity, dissipativity and flux conservation. For a class of Voronoi finite volume meshes we investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the discrete free energy to its equilibrium value with a unified rate of decay for this class of discretizations. The essential idea is an estimate of the free energy by the dissipation rate which is proved indirectly by taking into account sequences of Voronoi finite volume meshes. Essential ingredient in that proof is a discrete Sobolev-Poincaré inequality.

  • A. Caiazzo, M. Fernandez, J.-F. Gerbeau, V. Martin, Projection schemes for fluid flows through a porous interface, SIAM Journal on Scientific Computing, 33 (2011), pp. 541--564.

  • A. Caiazzo, M.A. Fernandez, V. Martin, Analysis of a stabilized finite element method for fluid flows through a porous interface, Applied Mathematics Letters, 24 (2011), pp. 2124--2127.

  • S. Amiranashvili, A.G. Vladimirov, U. Bandelow, A model equation for ultrashort optical pulses around the zero dispersion frequency, The European Physical Journal D. Atomic, Molecular, Optical and Plasma Physics, 58 (2010), pp. 219--226.
    Abstract
    The nonlinear Schrödinger equation based on the Taylor approximation of the material dispersion can become invalid for ultrashort and few-cycle optical pulses. Instead, we use a rational fit to the dispersion function such that the resonances are naturally accounted for. This approach allows us to derive a simple non-envelope model for short pulses propagating in one spatial dimension. This model is further investigated numerically and analytically.

  • S. Amiranashvili, U. Bandelow, A. Mielke, Padé approximant for refractive index and nonlocal envelope equations, Optics Communications, 283 (2010), pp. 480--485.
    Abstract
    Padé approximant is superior to Taylor expansion when functions contain poles. This is especially important for response functions in complex frequency domain, where singularities are present and intimately related to resonances and absorption. Therefore we introduce a diagonal Padé approximant for the complex refractive index and apply it to the description of short optical pulses. This yields a new nonlocal envelope equation for pulse propagation. The model offers a global representation of arbitrary medium dispersion and absorption, e.g., the fulfillment of the Kramers-Kronig relation can be established. In practice, the model yields an adequate description of spectrally broad pulses for which the polynomial dispersion operator diverges and can induce huge errors.

  • J. Härdtlein, C. Pflaum, A. Linke, C.H. Wolters, Advanced expression templates programming, Computing and Visualization in Science, 13 (2010), pp. 59--68.

  • H.-G. Purwins, H. Bödeker, S. Amiranashvili, Dissipative solitons, Advances in Physics, 59 (2010), pp. 485--701.

  • J. Fuhrmann, A. Fiebach, A. Erdmann, P. Trefonas, Acid diffusion effects between resists in freezing processes used for contact hole patterning, Microelectronic Engineering, 87 (2010), pp. 951--954.
    Abstract
    Double patterning following an litho?litho-etch scheme is a possible option to create structure widths below the nominal resolution of optical light with current exposure technology. Interactions between the first and second resist layers may influence the final structure created. In this paper, we perform a model based investigation of the possible consequences of the diffusion of photo-generated acid from the second resist to the first one. As a consequence, less acid is available for the deprotection reaction, and we observe a tendency to an increase of the CD values of the primary structure. We attempt to explain observed footing effects in contact holes by this effect.

  • A. Glitzky, J.A. Griepentrog, Discrete Sobolev--Poincaré inequalities for Voronoi finite volume approximations, SIAM Journal on Numerical Analysis, 48 (2010), pp. 372--391.
    Abstract
    We prove a discrete Sobolev-Poincare inequality for functions with arbitrary boundary values on Voronoi finite volume meshes. We use Sobolev's integral representation and estimate weakly singular integrals in the context of finite volumes. We establish the result for star shaped polyhedral domains and generalize it to the finite union of overlapping star shaped domains. In the appendix we prove a discrete Poincare inequality for space dimensions greater or equal to two.

  • A. Glitzky, K. Gärtner, Existence of bounded steady state solutions to spin-polarized drift-diffusion systems, SIAM Journal on Mathematical Analysis, 41 (2010), pp. 2489--2513.
    Abstract
    We study a stationary spin-polarized drift-diffusion model for semiconductor spintronic devices. This coupled system of continuity equations and a Poisson equation with mixed boundary conditions in all equations has to be considered in heterostructures. In 3D we prove the existence and boundedness of steady states. If the Dirichlet conditions are compatible or nearly compatible with thermodynamic equilibrium the solution is unique. The same properties are obtained for a space discretized version of the problem: Using a Scharfetter-Gummel scheme on 3D boundary conforming Delaunay grids we show existence, boundedness and, for small applied voltages, the uniqueness of the discrete solution.

  • V. John, M. Roland, On the impact of the scheme for solving the higher-dimensional equation in coupled population balance systems, International Journal for Numerical Methods in Engineering, 82 (2010), pp. 1450--1474.

  • A. Mielke, L. Paoli, A. Petrov, U. Stefanelli, Error estimates for space-time discretizations of a rate-independent variational inequality, SIAM Journal on Numerical Analysis, 48 (2010), pp. 1625--1646.
    Abstract
    This paper deals with error estimates for space-time discretizations in the context of evolutionary variational inequalities of rate-independent type. After introducing a general abstract evolution problem, we address a fully-discrete approximation and provide a priori error estimates. The application of the abstract theory to a semilinear case is detailed. In particular, we provide explicit space-time convergence rates for the isothermal Souza-Auricchio model for shape-memory alloys.

  • H. Si, J. Fuhrmann, K. Gärtner, Boundary conforming Delaunay mesh generation, Computational Mathematics and Mathematical Physics, 50 (2010), pp. 38--53.

  • S. Amiranashvili, U. Bandelow, A. Mielke, Padé approximant for refractive index and nonlocal envelope equations, Optics Communications, 283 (2009), pp. 480--485.
    Abstract
    Padé approximant is superior to Taylor expansion when functions contain poles. This is especially important for response functions in complex frequency domain, where singularities are present and intimately related to resonances and absorption. Therefore we introduce a diagonal Padé approximant for the complex refractive index and apply it to the description of short optical pulses. This yields a new nonlocal envelope equation for pulse propagation. The model offers a global representation of arbitrary medium dispersion and absorption, e.g., the fulfillment of the Kramers-Kronig relation can be established. In practice, the model yields an adequate description of spectrally broad pulses for which the polynomial dispersion operator diverges and can induce huge errors.

  • A.G. Vladimirov, A. Pimenov, D. Rachinskii, Numerical study of dynamical regimes in a monolithic passively mode locked semiconductor laser, IEEE J. Quantum Electron., 45 (2009), pp. 462--468.

  • G. Kozyreff, M. Tlidi, A. Mussot, E. Louvergneaux, M. Taki, A.G. Vladimirov, Localized beating between dynamically generated frequencies, Physical Review Letters, 102 (2009), pp. 043905/1--043905/4.

  • M. Tlidi, A.G. Vladimirov, D. Pieroux, D. Turaev, Spontaneous motion of cavity solitons induced by a delayed feedback, Physical Review Letters, 103 (2009), pp. 103904/1--103904/4.

  • M. Ehrhardt, H. Han, Ch. Zheng, Numerical simulation of waves in periodic structures, Communications in Computational Physics, 5 (2009), pp. 849--872.
    Abstract
    In this work we present a new numerical technique for solving periodic structure problems. This new approach possesses several advantages. First, it allows for a fast evaluation of the Robin-to-Robin operator for periodic array problems. Secondly, this computational method can also be used for bi-periodic structure problems with local defects. Our strategy is an improvement of the recently developed recursive doubling process by Yuan and Lu.
    In this paper we consider several problems, such as the exterior elliptic problems with strong coercivity, the time-dependent Schrödinger equation and finally the Helmholtz equation with damping.

  • J. Fuhrmann, A. Erdmann, Ch.R. Szmanda, A. Fiebach, M. Uhle, A model of self-limiting residual acid diffusion for pattern doubling, Microelectronic Engineering, 86 (2009), pp. 792--795.

  • J. Fuhrmann, A. Linke, H. Langmach, H. Baltruschat, Numerical calculation of the limiting current for a cylindrical thin layer flow cell, Electrochimica Acta, 55 (2009), pp. 430--438.

  • K. Gärtner, Existence of bounded discrete steady state solutions of the van Roosbroeck system on boundary conforming Delaunay grids, SIAM Journal on Scientific Computing, 31 (2009), pp. 1347--1362.
    Abstract
    The classic van Roosbroeck system describes the carrier transport in semiconductors in a drift diffusion approximation. Its analytic steady state solutions fulfill bounds for some mobility and recombination/generation models. The main goal of this paper is to establish the identical bounds for discrete in space, steady state solutions on 3d boundary conforming Delaunay grids and the classical Scharfetter-Gummel-scheme. Together with a uniqueness proof for small applied voltages and the known dissipativity (continuous as well as space and time discrete) these discretization techniques carry over the essential analytic properties to the discrete case. The proofs are of interest for deriving averaging schemes for space or state dependent material parameters, which are preserving these qualitative properties, too. To illustrate the properties of the scheme 1, 4, 16 elementary cells of a modified CoolMOS like structure are depleted by increasing the applied voltage until steady state avalanche breakdown occurs.

  • A. Glitzky, K. Gärtner, Energy estimates for continuous and discretized electro-reaction-diffusion systems, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 70 (2009), pp. 788--805.
    Abstract
    We consider electro-reaction-diffusion systems consisting of continuity equations for a finite number of species coupled with a Poisson equation. We take into account heterostructures, anisotropic materials and rather general statistic relations.
    We investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the free energy to its equilibrium value. Here the essential idea is an estimate of the free energy by the dissipation rate which is proved indirectly.
    The same properties are shown for an implicit time discretized version of the problem. Moreover, we provide a space discretized scheme for the electro-reaction-diffusion system which is dissipative (the free energy decays monotonously). On a fixed grid we use for each species different Voronoi boxes which are defined with respect to the anisotropy matrix occurring in the flux term of this species.

  • A. Glitzky, Energy estimates for electro-reaction-diffusion systems with partly fast kinetics, Discrete and Continuous Dynamical Systems, 25 (2009), pp. 159--174.
    Abstract
    We start from a basic model for the transport of charged species in heterostructures containing the mechanisms diffusion, drift and reactions in the domain and at its boundary. Considering limit cases of partly fast kinetics we derive reduced models. This reduction can be interpreted as some kind of projection scheme for the weak formulation of the basic electro--reaction--diffusion system. We verify assertions concerning invariants and steady states and prove the monotone and exponential decay of the free energy along solutions to the reduced problem and to its fully implicit discrete-time version by means of the results of the basic problem. Moreover we make a comparison of prolongated quantities with the solutions to the basic model.

  • V. John, T. Mitkova, M. Roland, K. Sundmacher, L. Tobiska, A. Voigt, Simulations of population balance systems with one internal coordinate using finite element methods, Chemical Engineering Sciences, 64 (2009), pp. 733--741.

  • A. Mielke, T. Roubíček, Numerical approaches to rate-independent processes and applications in inelasticity, ESAIM: Mathematical Modelling and Numerical Analysis, 43 (2009), pp. 399--429.
    Abstract
    A general abstract approximation scheme for rate-independent processes in the energetic formulation is proposed and its convergence is proved under various rather mild data qualifications. The abstract theory is illustrated on several examples: plasticity with isotropic hardening, damage, debonding, magnetostriction, and two models of martensitic transformation in shape-memory alloys.

  • H. Stephan, Modeling of drift-diffusion systems, ZAMP Zeitschrift fur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Mathematiques et de Physique Appliquees, 60 (2009), pp. 33--53.
    Abstract
    We derive drift-diffusion systems describing transport processes starting from free energy and equilibrium solutions by a unique method. We include several statistics, heterostructures and cross diffusion. The resulting systems of nonlinear partial differential equations conserve mass and positivity, and have a Lyapunov function (free energy). Using the inverse Hessian as mobility, non-degenerate diffusivity matrices turn out to be diagonal, or - in the case of cross diffusion - even constant.

  • S. Amiranashvili, A.G. Vladimirov, U. Bandelow, Solitary-wave solutions for few-cycle optical pulses, Physical Review A, 77 (2008), pp. 063821/1--063821/7.

  • M. Pietrzyk, I. Kanattšikow, U. Bandelow, On the propagation of vector ultra-short pulses, Journal of Nonlinear Mathematical Physics, 15 (2008), pp. 162-170.

  • R. Čiegis, M. Radziunas, M. Lichtner, Numerical algorithms for simulation of multisection lasers by using traveling wave model, IEEE J. Select. Topics Quantum Electron., 13 (2008), pp. 327-348.

  • D. Turaev, M. Radziunas, A.G. Vladimirov, Chaotic soliton walk in periodically modulated media, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 77 (2008), pp. 06520/1--06520/4.

  • A. Glitzky, Exponential decay of the free energy for discretized electro-reaction-diffusion systems, Nonlinearity, 21 (2008), pp. 1989--2009.
    Abstract
    Our focus are electro-reaction-diffusion systems consisting of continuity equations for a finite number of species coupled with a Poisson equation. We take into account heterostructures, anisotropic materials and rather general statistical relations. We introduce a discretization scheme (in space and fully implicit in time) using a fixed grid but for each species different Voronoi boxes which are defined with respect to the anisotropy matrix occurring in the flux term of this species. This scheme has the special property that it preserves the main features of the continuous systems, namely positivity, dissipativity and flux conservation. For the discretized electro-reaction-diffusion system we investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the free energy to its equilibrium value. The essential idea is an estimate of the free energy by the dissipation rate which is proved indirectly.

  • O. Minet, H. Gajewski, J.A. Griepentrog, J. Beuthan, The analysis of laser light scattering during rheumatoid arthritis by image segmentation, Laser Physics Letters, 4 (2007), pp. 604--610.

  • M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A.G. Vladimirov, M. Taki, Control and removing of modulational instabilities in low dispersion photonic crystal fiber cavities, Optics Letters, 32 (2007), pp. 662-664.

  • D. Turaev, A.G. Vladimirov, S. Zelik, Chaotic bound state of localized structures in the complex Ginzburg--Landau equation, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 75 (2007), pp. 045601/1-045601/4.

  • M. Lichtner, M. Radziunas, L. Recke, Well-posedness, smooth dependence and center manifold reduction for a semilinear hyperbolic system from laser dynamics, Mathematical Methods in the Applied Sciences, 30 (2007), pp. 931--960.

  • A.G. Vladimirov, D.V. Skryabin, G. Kozyreff, P. Mandel, M. Tlidi, Bragg localized structures in a passive cavity with transverse modulation of the refractive index and the pump, Optics Express, 14 (2006), pp. 1--6.

  • H. Gajewski, J.A. Griepentrog, A descent method for the free energy of multicomponent systems, Discrete and Continuous Dynamical Systems, 15 (2006), pp. 505--528.

  • M. Kočvara, A. Mielke, T. Roubíček, A rate-independent approach to the delamination problem, Mathematics and Mechanics of Solids, 11 (2006), pp. 423--447.

  • U. Bandelow, M. Radziunas, A. Vladimirov, B. Hüttl, R. Kaiser, 40 GHz Mode-locked semiconductor lasers: Theory, simulations and experiment, Optical and Quantum Electronics, 38 (2006), pp. 495--512.

  • M. Radziunas, F. Ivanauskas, The convergence and stability of splitting finite difference schemes for nonlinear evolutionary type equations, Optical and Quantum Electronics, 45 (2005), pp. 334--352.

  • P. Evans, A. Münch, Interaction of advancing fronts and meniscus profiles formed by surface-tension-gradient-driven liquid films, SIAM Journal on Applied Mathematics, 66 (2006), pp. 1610-1631.

  • A. Münch, Dewetting rates of thin liquid films, Physics of Fluids, 17 (2005), pp. S309--S318.

  • N. Nefedov, M. Radziunas, K.R. Schneider, A. Vasil'eva, Change of the type of contrast structures in parabolic Neumann problems, Computational Mathematics and Mathematical Physics, 45 (2005), pp. 37--51.

  • W. Dreyer, B. Wagner, Sharp-interface model for eutectic alloys. Part I: Concentration dependent surface tension, Interfaces and Free Boundaries. Mathematical Modelling, Analysis and Computation, 7 (2005), pp. 199--227.

  • N. Nefedov, M. Radziunas, K.R. Schneider, Analytic-numerical investigation of delayed exchange of stabilities in singularly perturbed parabolic problems, Computational Mathematics and Mathematical Physics, 44 (2004), pp. 1213-1220.

  • A. Rathsfeld, R. Schneider, On a quadrature algorithm for the piecewise linear wavelet collocation applied to boundary integral equations, Mathematical Methods in the Applied Sciences, 26 (2003), pp. 937--979.

  • A.M. Krasnosel'skii, D.I. Rachinskii, K.R. Schneider, Hopf bifurcations in resonance 2:1, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 52A (2003), pp. 943--960.

  • G. Mastroianni, C. Frammartino, A. Rathsfeld, On polynomial collocation for second kind integral equations with fixed singularities of Mellin type, Numerische Mathematik, 94 (2003), pp. 333--365.

  • N.N. Nefedov, K.R. Schneider, Delay of exchange of stabilities in singularly perturbed parabolic problems, Proceedings of the Steklov Institute of Mathematics, (2003), pp. S144-S154.

  • M. Tlidi, A.G. Vladimirov, P. Mandel, Interaction and stability of periodic and localized structures in optical bistable systems, IEEE J. Quantum Electron., 39 (2003), pp. 197--205.

  • H. Gajewski, K. Gärtner, Domain separation by means of sign changing eigenfunctions of $p$-Laplacians, Applicable Analysis. An International Journal, 79 (2001), pp. 483--501.

  • W. Dreyer, W.H. Müller, A study of the coarsening in tin/lead solders, International Journal of Solids and Structures, 37 (2000), pp. 3841--3871.

  Contributions to Collected Editions

  • M. Liero, J. Fuhrmann, A. Glitzky, Th. Koprucki, A. Fischer, S. Reineke, Modeling and simulation of electrothermal feedback in large-area organic leds, in: Proceedings of ``the 17th International Conference on Numerical Simulation of Optoelectronic Devices'', J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 105--106, DOI 10.1109/NUSOD.2017.8010013 .

  • N. Ahmed, A. Linke, Ch. Merdon, Towards pressure-robust mixed methods for the incompressible Navier--Stokes equations, in: Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects FVCA 8, Lille, France, June 2017, C. Cances, P. Omnes, eds., 199 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2017, pp. 351--359.

  • P. Farrell, Th. Koprucki, J. Fuhrmann, Comparison of consistent flux discretizations for drift diffusion beyond boltzmann statistics, in: Proceedings of ``the 17th International Conference on Numerical Simulation of Optoelectronic Devices'', J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 219--220, DOI 10.1109/NUSOD.2017.8010070 .

  • J. Fuhrmann, A. Glitzky, M. Liero, Hybrid finite-volume/finite-element schemes for p(x)-Laplace thermistor models, in: Finite Volumes for Complex Applications VIII -- Hyperbolic, Elliptic and Parabolic Problems -- FVCA 8, Lille, France, June 2017, C. Cancès, P. Omnes, eds., 200 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2017, pp. 397--405, DOI 10.1007/978-3-319-57394-6_42 .

  • J. Fuhrmann, C. Guhlke, A finite volume scheme for Nernst--Planck--Poisson systems with Ion size and solvation effects, in: Finite Volumes for Complex Applications VIII -- Hyperbolic, Elliptic and Parabolic Problems -- FVCA 8, Lille, France, June 2017, C. Cancès, P. Omnes, eds., 200 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2017, pp. 497--505, DOI 10.1007/978-3-319-57394-6_52 .

  • M. Kantner, U. Bandelow, Th. Koprucki, H.-J. Wünsche, Multi-scale modelling and simulation of single-photon sources on a device level, in: Euro-TMCS II -- Theory, Modelling & Computational Methods for Semiconductors, 7th -- 9th December 2016, Tyndall National Institute, University College Cork, Ireland, E. O'Reilly, S. Schulz, S. Tomic, eds., Tyndall National Institute, 2016, pp. 65.

  • S. Ganesan, V. John, G. Matthies, R. Meesala, A. Shamim, U. Wilbrandt, An object oriented parallel finite element scheme for computations of PDEs: Design and implementation, in: 2016 IEEE 23rd International Conference on High Performance Computing Workshops (PDF only), pp. 106--115, DOI 10.1109/HiPCW.2016.19 .

  • G. Lazzaroni, R. Rossi, M. Thomas, R. Toader, Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics, in: MURPHYS-HSFS-2014: 7th International Workshop on MUlti-Rate Processes and HYSteresis (MURPHYS) & 2nd International Workshop on Hysteresis and Slow-Fast Systems (HSFS), O. Klein, M. Dimian, P. Gurevich, D. Knees, D. Rachinskii, S. Tikhomirov, eds., 727 of Journal of Physics: Conference Series, IOP Publishing, 2016, pp. 012009/1--012009/20.
    Abstract
    This note deals with the analysis of a model for partial damage, where the rate-independent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from [Roubíček M2AS'09, SIAM'10] with the methods from Lazzaroni/Rossi/Thomas/Toader [WIAS Preprint 2025]. The present analysis encompasses, differently from [Roubíček SIAM'10], the monotonicity in time of damage and the dependence of the viscous tensor on damage and temperature, and, unlike [WIAS Preprint 2025], a nonconstant heat capacity and a time-dependent Dirichlet loading.

  • A. Caiazzo, J. Mura, A two-scale homogenization approach for the estimation of porosity in elastic media subject area, in: Trends in Differential Equations and Applications, F.O. Gallego, M.V. Redondo Neble, J.R.R. Galván, eds., 8 of SEMA SIMAI Springer Series, Springer International Publishing Switzerland, Cham, 2016, pp. 89--105.

  • P. Farrell, N. Rotundo, D.H. Doan, M. Kantner, J. Fuhrmann, Th. Koprucki, Numerical methods for drift-diffusion models, in: Handbook of Optoelectronic Device Modeling and Simulation (Two-Volume Set), J. Piprek, ed., Series in Optics and Optoelectronics, CRC Press Taylor & Francis Group, 2017.
    Abstract
    The van Roosbroeck system describes the semi-classical transport of free electrons and holes in a self-consistent electric field using a drift-diffusion approximation. It became the standard model to describe the current flow in semiconductor devices at macroscopic scale. Typical devices modeled by these equations range from diodes, transistors, LEDs, solar cells and lasers to quantum nanostructures and organic semiconductors. The report provides an introduction into numerical methods for the van Roosbroeck system. The main focus lies on the Scharfetter-Gummel finite volume discretization scheme and recent efforts to generalize this approach to general statistical distribution functions.

  • A. Mielke, Free energy, free entropy, and a gradient structure for thermoplasticity, in: Innovative Numerical Approaches for Multi-Field and Multi-Scale Problems. In Honor of Michael Ortiz's 60th Birthday, K. Weinberg, A. Pandolfi, eds., 81 of Lecture Notes in Applied and Computational Mechanics, Springer International Publishing Switzerland, Cham, 2016, pp. 135--160.
    Abstract
    In the modeling of solids the free energy, the energy, and the entropy play a central role. We show that the free entropy, which is defined as the negative of the free energy divided by the temperature, is similarly important. The derivatives of the free energy are suitable thermodynamical driving forces for reversible (i.e. Hamiltonian) parts of the dynamics, while for the dissipative parts the derivatives of the free entropy are the correct driving forces. This difference does not matter for isothermal cases nor for local materials, but it is relevant in the non-isothermal case if the densities also depend on gradients, as is the case in gradient thermoplasticity.

    Using the total entropy as a driving functional, we develop gradient structures for quasistatic thermoplasticity, which again features the role of the free entropy. The big advantage of the gradient structure is the possibility of deriving time-incremental minimization procedures, where the entropy-production potential minus the total entropy is minimized with respect to the internal variables and the temperature.

    We also highlight that the usage of an auxiliary temperature as an integrating factor in Yang/Stainier/Ortiz "A variational formulation of the coupled thermomechanical boundary-value problem for general dissipative solids" (J. Mech. Physics Solids, 54, 401-424, 2006) serves exactly the purpose to transform the reversible driving forces, obtained from the free energy, into the needed irreversible driving forces, which should have been derived from the free entropy. This reconfirms the fact that only the usage of the free entropy as driving functional for dissipative processes allows us to derive a proper variational formulation.

  • D. Peschka, Numerics of contact line motion for thin films, in: 8th Vienna International Conference on Mathematical Modelling -- MATHMOD 2015, 48 of IFAC-PapersOnLine, Elsevier, 2015, pp. 390--393.

  • W. Huang, L. Kamenski, J. Lang, Stability of explicit Runge--Kutta methods for high order finite element approximation of linear parabolic equations, in: Numerical Mathematics and Advanced Applications -- ENUMATH 2013, A. Abdulle, S. Deparis, D. Kressner, F. Nobile, M. Picasso, eds., 103 of Lecture Notes in Computational Science and Engineering, Springer International Publishing, Cham [et al.], 2015, pp. 165--173.
    Abstract
    We study the stability of explicit Runge-Kutta methods for high order Lagrangian finite element approximation of linear parabolic equations and establish bounds on the largest eigenvalue of the system matrix which determines the largest permissible time step. A bound expressed in terms of the ratio of the diagonal entries of the stiffness and mass matrices is shown to be tight within a small factor which depends only on the dimension and the choice of the reference element and basis functions but is independent of the mesh or the coefficients of the initial-boundary value problem under consideration. Another bound, which is less tight and expressed in terms of mesh geometry, depends only on the number of mesh elements and the alignment of the mesh with the diffusion matrix. The results provide an insight into how the interplay between the mesh geometry and the diffusion matrix affects the stability of explicit integration schemes when applied to a high order finite element approximation of linear parabolic equations on general nonuniform meshes.

  • R.M. Arkhipov, M. Radziunas, A.G. Vladimirov, Theoretical analysis of the influence of external periodic forcing on nonlinear dynamics of passively mode-locked semiconductor lasers, in: Proceedings of the XIV School Seminar Wave Phenomena in Inhomogeneous Media (Waves 2014), Section 9, Nonlinear dynamics and information systems (in electronic form and in Russian), 2014, pp. 3--6.

  • R.M. Arkhipov, M.V. Arkhipov, Mode-locking in two section and single section lasers due to coherent interaction of light and matter in the gain and absorbing media, in: Proceedings of the XIV School Seminar Wave Phenomena in Inhomogeneous Media (Waves 2014), Section 3, Nonlinear and coherent optics (in electronic form and in Russian), 2014, pp. 43--45.

  • TH. Koprucki, M. Kantner, J. Fuhrmann, K. Gärtner, On modifications of the Scharfetter--Gummel scheme for drift-diffusion equations with Fermi-like statistical distribution functions, in: Proceedings of the 14th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2014, 1--4 September 2014, J. Piprek, J. Javaloyes, eds., IEEE Conference Publications Management Group, Piscataway, NJ, USA, 2014, pp. 155--156.

  • A. Glitzky, A. Mielke, L. Recke, M. Wolfrum, S. Yanchuk, D2 -- Mathematics for optoelectronic devices, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 243--256.

  • J. Fuhrmann, A. Linke, Ch. Merdon, Coupling of fluid flow and solute transport using a divergence-free reconstruction of the Crouzeix--Raviart element, in: Finite Volumes for Complex Applications VII -- Elliptic, Parabolic and Hyperbolic Problems -- FVCA 7, Berlin, June 2014, J. Fuhrmann, M. Ohlberger, Ch. Rohde, eds., 78 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2014, pp. 587--595.

  • K. Götze, Free fall of a rigid body in a viscoelastic fluid, in: Geophysical Fluid Dynamics, Workshop, February 18--22, 2013, 10 of Oberwolfach Reports, Mathematisches Forschungsinstitut Oberwolfach, 2013, pp. 554--556.

  • R.M. Arkhipov, M. Radziunas, A.G. Vladimirov, Numerical simulation of passively mode-locked semiconductor lasers under dual mode optical injection regime, in: Proceedings of the Conference ICONO/LAT 2013 (Technical Digest on CD ROM), Section LAT-01: Solid-State Lasers, Materials and Applications, Russian Academy of Sciences, Moscow, 2013, pp. 111--112.

  • R.M. Arkhipov, I. Babushkin, M.V. Arkhipov , Y.A. Tolmachev, Spectral and temporal characteristics of radiation from a periodic resonant medium excited at the superluminal velocity, in: Proceedings of the Conference ICONO/LAT 2013 (Technical Digest on CD ROM), Section LAT-04: Diffractive Optics and Nanophotonics, Russian Academy of Sciences, Moscow, 2013, pp. 14--15.

  • TH. Koprucki, K. Gärtner, Generalization of the Scharfetter--Gummel scheme, in: Proceedings of the 13th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2013, 19--22 August 2013, J. Piprek, L. Chrostowski, eds., IEEE Conference Publications Management Group, Piscataway, NJ, USA, 2013, pp. 85--86.

  • C. Carstensen, C. Merdon, J. Neumann, Aspects of guaranteed error control in CPDE, in: Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications, O.P. Iliev, S.D. Margenov, P.D. Minev, P.S. Vassilevski, L.T. Zikatanov, eds., 45 of Springer Proceedings in Mathematics & Statistics, Springer, New York, 2013, pp. 103--119.

  • A. Mielke, Gradient structures and dissipation distances for reaction-diffusion systems, in: Material Theory, Workshop, Dezember 16--20, 2013, A. Desimone, S. Luckhaus, L. Truskinovsky, eds., 10 of Oberwolfach Reports, Mathematisches Forschungsinstitut Oberwolfach, 2013, pp. 3455--3458.

  • TH. Koprucki, K. Gärtner, Discretization scheme for drift-diffusion equations with strong diffusion enhancement, in: Proceedings of the 12th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD'12, J. Piprek, W. Lu, eds., IEEE Conference Publications Management Group, New Jersey, USA, 2012, pp. 103--104.

  • A. Glitzky, J.A. Griepentrog, On discrete Sobolev--Poincaré inequalities for Voronoi finite volume approximations, in: Finite volumes for complex applications VI: Problems and perspectives, J. Fořt, J. Fürst, J. Halama, R. Herbin, F. Hubert, eds., Springer Proceedings in Mathematics 4, Springer, Heidelberg, 2011, pp. 533--541.

  • S. Bartels, R. Müller, Die kalte Zunge, in: Besser als Mathe --- Moderne angewandte Mathematik aus dem MATHEON zum Mitmachen, K. Biermann, M. Grötschel, B. Lutz-Westphal, eds., Reihe: Populär, Vieweg+Teubner, Wiesbaden, 2010, pp. 227--235.

  • M. Jensen, R. Müller, Stable Crank--Nicolson discretisation for incompressible miscible displacement problems of low regularity, in: Numerical Mathematics and Advanced Applications 2009, Part 2, G. Kreiss, P. Lötstedt, A. Målqvist, M. Neytcheva, eds., Springer, Heidelberg et al., pp. 469--477.
    Abstract
    In this article we study the numerical approximation of incompressible miscible displacement problems with a linearised Crank-Nicolson time discretisation, combined with a mixed finite element and discontinuous Galerkin method. At the heart of the analysis is the proof of convergence under low regularity requirements. Numerical experiments demonstrate that the proposed method exhibits second-order convergence for smooth and robustness for rough problems.

  • D. Turaev, A.G. Vladimirov, S. Zelik, Strong enhancement of interaction of optical pulses induced by oscillatory instability, in: CLEO/Europe and EQEC 2009 Conference Digest (Optical Society of America, 2009), poster EH.P.13 WED, 2009, pp. 1--1.

  • J. Fuhrmann, K. Gärtner, Modeling of two-phase flow and catalytic reaction kinetics for DMFCs, in: Device and Materials Modeling in PEM Fuel Cells, S. Paddison, K. Promislow, eds., 113 of Topics in Applied Physics, Springer, Berlin/Heidelberg, 2009, pp. 297--316.

  • H. Gajewski, J.A. Griepentrog, A. Mielke, J. Beuthan, U. Zabarylo, O. Minet, Image segmentation for the investigation of scattered-light images when laser-optically diagnosing rheumatoid arthritis, in: Mathematics -- Key Technology for the Future, W. Jäger, H.-J. Krebs, eds., Springer, Heidelberg, 2008, pp. 149--161.

  • M. Ehrhardt, J. Fuhrmann, A. Linke, E. Holzbecher, Mathematical modeling of channel-porous layer interfaces in PEM fuel cells, in: Proceedings of FDFC2008 --- Fundamentals and Developments of Fuel Cell Conference 2008, Nancy, France, December 10--12 (CD), 2008, pp. 8 pages.
    Abstract
    In proton exchange membrane (PEM) fuel cells, the transport of the fuel to the active zones, and the removal of the reaction products are realized using a combination of channels and porous diffusion layers. In order to improve existing mathematical and numerical models of PEM fuel cells, a deeper understanding of the coupling of the flow processes in the channels and diffusion layers is necessary.
    After discussing different mathematical models for PEM fuel cells, the work will focus on the description of the coupling of the free flow in the channel region with the filtration velocity in the porous diffusion layer as well as interface conditions between them.
    The difficulty in finding effective coupling conditions at the interface between the channel flow and the membrane lies in the fact that often the orders of the corresponding differential operators are different, e.g., when using stationary (Navier-)Stokes and Darcy's equation. Alternatively, using the Brinkman model for the porous media this difficulty does not occur.
    We will review different interface conditions, including the well-known Beavers-Joseph-Saffman boundary condition and its recent improvement by Le Bars and Worster.

  • A. Mielke, Numerical approximation techniques for rate-independent inelasticity, in: Proceedings of the IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media, B.D. Reddy, ed., 11 of IUTAM Bookseries, Springer, 2008, pp. 53--63.

  • A. Mussot, M. Tlidi, E. Louvergneaux, G. Kozyref, A.G. Vladimirov, M. Taki, Removing modulational instabilities in low dispersion fiber cavities, in: 2007 European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference (CLEO® / Europe-IQEC) Conference Digest (oral presentation CD-9-WED), IEEE, 2007, pp. 1--1.

  • A.G. Vladimirov, D.V. Skryabin, M. Tlidi, Localized structures of light in nonlinear devices with intracavity photonic bandgap material, in: 2007 European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference (CLEO®/Europe-IQEC) Conference Digest (oral presentation IG-4-MON), IEEE, 2007, pp. 1--1.

  • U. Bandelow, H. Gajewski, R. Hünlich, Thermodynamic designed energy model, in: Proceedings of the IEEE/LEOS 3rd International Conference on Numerical Simulation of Semiconductor Optoelectronic Devices (NUSOD'03), J. Piprek, ed., 2003, pp. 35--37.

  • H. Gajewski, H.-Chr. Kaiser, H. Langmach, R. Nürnberg, R.H. Richter, Mathematical modelling and numerical simulation of semiconductor detectors, in: Mathematics --- Key Technology for the Future. Joint Projects Between Universities and Industry, W. Jäger, H.-J. Krebs, eds., Springer, Berlin [u.a.], 2003, pp. 355--364.

  • R. Hünlich, G. Albinus, H. Gajewski, A. Glitzky, W. Röpke, J. Knopke, Modelling and simulation of power devices for high-voltage integrated circuits, in: Mathematics --- Key Technology for the Future. Joint Projects Between Universities and Industry, W. Jäger, H.-J. Krebs, eds., Springer, Berlin [u.a.], 2003, pp. 401--412.

  • H. Gajewski, An application of eigenfunctions of $p$-Laplacians to domain separation, in: Proceedings of Partial Differential Equations and Applications. A conference held in honor of the 70th birthday of Professor Jindřich Nečas, Olomouc, December 13--17, 1999, Š. Nečasová, H. Petzeltová, N. Pokorný, A. Sequeira, eds., 126 of Math. Bohem., Academy of Sciences of the Czech Republic, Mathematical Institute, Prague, 2001, pp. 395--401.

  Preprints, Reports, Technical Reports

  • P.L. Lederer, Ch. Merdon, J. Schöberl, Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods, Preprint no. 2462, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2462 .
    Abstract, PDF (854 kByte)
    Recent works showed that pressure-robust modifications of mixed finite element methods for the Stokes equations outperform their standard versions in many cases. This is achieved by divergence-free reconstruction operators and results in pressure-independent velocity error estimates which are robust with respect to small viscosities. In this paper we develop a posteriori error control which reflects this robustness.

  • P.W. Schroeder, Ch. Lehrenfeld, A. Linke, G. Lube, Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier--Stokes equations, Preprint no. 2436, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2436 .
    Abstract, PDF (798 kByte)
    Inf-sup stable FEM applied to time-dependent incompressible Navier--Stokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressure-robustness ensures the fulfilment of a fundamental invariance principle and velocity error estimates are not corrupted by the pressure approximability. Secondly, Re-semi-robustness means that constants appearing on the right-hand side of kinetic and dissipation energy error estimates (including Gronwall constants) do not explicitly depend on the Reynolds number. Such estimates rely on an essential regularity assumption for the gradient of the velocity, which is discussed in detail. In the sense of best practice, we review and establish pressure- and Re-semi-robust estimates for pointwise divergence-free H1-conforming FEM (like Scott--Vogelius pairs or certain isogeometric based FEM) and pointwise divergence-free H(div)-conforming discontinuous Galerkin FEM. For convection-dominated problems, the latter naturally includes an upwind stabilisation for the velocity which is not gradient-based.

  • P. Farrell, M. Patriarca, J. Fuhrmann, Th. Koprucki, Comparison of thermodynamically consistent charge carrier flux discretizations for Fermi--Dirac and Gauss--Fermi statistics, Preprint no. 2424, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2424 .
    Abstract, PDF (1572 kByte)
    We compare three thermodynamically consistent Scharfetter--Gummel schemes for different distribution functions for the carrier densities, including the Fermi--Dirac integral of order 1/2 and the Gauss--Fermi integral. The most accurate (but unfortunately also most costly) generalized Scharfetter--Gummel scheme requires the solution of an integral equation. We propose a new method to solve this integral equation numerically based on Gauss quadrature and Newton's method. We discuss the quality of this approximation and plot the resulting currents for Fermi--Dirac and Gauss--Fermi statistics. Finally, by comparing two modified (diffusion-enhanced and inverse activity based) Scharfetter--Gummel schemes with the more accurate generalized scheme, we show that the diffusion-enhanced ansatz leads to considerably lower flux errors, confirming previous results (J. Comp. Phys. 346:497-513, 2017).

  • V. John, P. Knobloch, J. Novo, Finite elements for scalar convection-dominated equations and incompressible flow problems -- A never ending story?, Preprint no. 2410, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2410 .
    Abstract, PDF (283 kByte)
    The contents of this paper is twofold. First, important recent results concerning finite element methods for convection-dominated problems and incompressible flow problems are described that illustrate the activities in these topics. Second, a number of, in our opinion, important problems in these fields are discussed.

  • N. Ahmed, C. Bartsch, V. John, U. Wilbrandt, An assessment of solvers for saddle point problems emerging from the incompressible Navier--Stokes equations, Preprint no. 2408, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2408 .
    Abstract, PDF (1086 kByte)
    Efficient incompressible flow simulations, using inf-sup stable pairs of finite element spaces, require the application of efficient solvers for the arising linear saddle point problems. This paper presents an assessment of different solvers: the sparse direct solver UMFPACK, the flexible GMRES (FGMRES) method with different coupled multigrid preconditioners, and FGMRES with Least Squares Commutator (LSC) preconditioners. The assessment is performed for steady-state and time-dependent flows around cylinders in 2d and 3d. Several pairs of inf-sup stable finite element spaces with second order velocity and first order pressure are used. It turns out that for the steady-state problems often FGMRES with an appropriate multigrid preconditioner was the most efficient method on finer grids. For the time-dependent problems, FGMRES with LSC preconditioners that use an inexact iterative solution of the velocity subproblem worked best for smaller time steps.

  • M. Heida, On convergences of the squareroot approximation scheme to the Fokker--Planck operator, Preprint no. 2399, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2399 .
    Abstract, PDF (506 kByte)
    We study the qualitative convergence properties of a finite volume scheme that recently was proposed by Lie, Fackeldey and Weber [SIAM Journal on Matrix Analysis and Applications 2013 (34/2)] in the context of conformation dynamics. The scheme was derived from physical principles and is called the squareroot approximation (SQRA) scheme. We show that solutions to the SQRA equation converge to solutions of the Fokker-Planck equation using a discrete notion of G-convergence. Hence the squareroot approximation turns out to be a usefull approximation scheme to the Fokker-Planck equation in high dimensional spaces. As an example, in the special case of stationary Voronoi tessellations we use stochastic two-scale convergence to prove that this setting satisfies the G-convergence property. In particular, the class of tessellations for which the G-convergence result holds is not trivial.

  • S. Bartels, M. Milicevic, M. Thomas, Numerical approach to a model for quasistatic damage with spatial $BV$-regularization, Preprint no. 2388, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2388 .
    Abstract, PDF (566 kByte)
    We address a model for rate-independent, partial, isotropic damage in quasistatic small strain linear elasticity, featuring a damage variable with spatial BV-regularization. Discrete solutions are obtained using an alternate time-discrete scheme and the Variable-ADMM algorithm to solve the constrained nonsmooth optimization problem that determines the damage variable at each time step. We prove convergence of the method and show that discrete solutions approximate a semistable energetic solution of the rate-independent system. Moreover, we present our numerical results for two benchmark problems.

  • A. Linke, Ch. Merdon, M. Neilan, F. Neumann, Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes problem, Preprint no. 2374, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2374 .
    Abstract, PDF (334 kByte)
    Nearly all classical inf-sup stable mixed finite element methods for the incompressible Stokes equations are not pressure-robust, i.e., the velocity error is dependent on the pressure. However, recent results show that pressure-robustness can be recovered by a non-standard discretization of the right hand side alone. This variational crime introduces a consistency error in the method which can be estimated in a straightforward manner provided that the exact velocity solution is sufficiently smooth. The purpose of this paper is to analyze the pressure-robust scheme with low regularity. The numerical analysis applies divergence-free H¹-conforming Stokes finite element methods as a theoretical tool. As an example, pressure-robust velocity and pressure a-priori error estimates will be presented for the (first order) nonconforming Crouzeix--Raviart element. A key feature in the analysis is the dependence of the errors on the Helmholtz projector of the right hand side data, and not on the entire data term. Numerical examples illustrate the theoretical results.

  • C. Bertoglio, A. Caiazzo, Y. Bazilevs, M. Braack, M. Esmaily-Moghadam, V. Gravemeier, A.L. Marsden, O. Pironneau, I.E. Vignon-Clementel, W.A. Wall, Benchmark problems for numerical treatment of backflow at open boundaries, Preprint no. 2372, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2372 .
    Abstract, PDF (3076 kByte)
    In computational fluid dynamics, incoming velocity at open boundaries, or backflow, often yields to unphysical instabilities already for moderate Reynolds numbers. Several treatments to overcome these backflow instabilities have been proposed in the literature. However, these approaches have not yet been compared in detail in terms of accuracy in different physiological regimes, in particular due to the difficulty to generate stable reference solutions apart from analytical forms. In this work, we present a set of benchmark problems in order to compare different methods in different backflow regimes (with a full reversal flow and with propagating vortices after a stenosis). The examples are implemented in FreeFem++ and the source code is openly available, making them a solid basis for future method developments.

  • N. Ahmed, A. Linke, Ch. Merdon, On really locking-free mixed finite element methods for the transient incompressible Stokes equations, Preprint no. 2368, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2368 .
    Abstract, PDF (388 kByte)
    Inf-sup stable mixed methods for the steady incompressible Stokes equations that relax the divergence constraint are often claimed to deliver locking-free discretizations. However, this relaxation leads to a pressure-dependent contribution in the velocity error, which is proportional to the inverse of the viscosity, thus giving rise to a (different) locking phenomenon. However, a recently proposed modification of the right hand side alone leads to a discretization that is really locking-free, i.e., its velocity error converges with optimal order and is independent of the pressure and the smallness of the viscosity. In this contribution, we extend this approach to the transient incompressible Stokes equations, where besides the right hand side also the velocity time derivative requires an improved space discretization. Semi-discrete and fully-discrete a-priori velocity and pressure error estimates are derived, which show beautiful robustness properties. Two numerical examples illustrate the superior accuracy of pressure-robust space discretizations in the case of small viscosities.

  • A. Alphonse, Ch.M. Elliott, J. Terra, A coupled ligand-receptor bulk-surface system on a moving domain: Well posedness, regularity and convergence to equilibrium, Preprint no. 2357, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2357 .
    Abstract, PDF (536 kByte)
    We prove existence, uniqueness, and regularity for a reaction-diffusion system of coupled bulk-surface equations on a moving domain modelling receptor-ligand dynamics in cells. The nonlinear coupling between the three unknowns is through the Robin boundary condition for the bulk quantity and the right hand sides of the two surface equations. Our results are new even in the non-moving setting, and in this case we also show exponential convergence to a steady state. The primary complications in the analysis are indeed the nonlinear coupling and the Robin boundary condition. For the well posedness and essential boundedness of solutions we use several De Giorgi-type arguments, and we also develop some useful estimates to allow us to apply a Steklov averaging technique for time-dependent operators to prove that solutions are strong. Some of these auxiliary results presented in this paper are of independent interest by themselves.

  • L. Adam, M. Hintermüller, Th.M. Surowiec, A semismooth Newton method with analytical path-following for the $H^1$-projection onto the Gibbs simplex, Preprint no. 2340, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2340 .
    Abstract, PDF (1345 kByte)
    An efficient, function-space-based second-order method for the $H^1$-projection onto the Gibbs-simplex is presented. The method makes use of the theory of semismooth Newton methods in function spaces as well as Moreau-Yosida regularization and techniques from parametric optimization. A path-following technique is considered for the regularization parameter updates. A rigorous first and second-order sensitivity analysis of the value function for the regularized problem is provided to justify the update scheme. The viability of the algorithm is then demonstrated for two applications found in the literature: binary image inpainting and labeled data classification. In both cases, the algorithm exhibits mesh-independent behavior.

  • L. Heltai, N. Rotundo, Error estimates in weighted Sobolev norms for finite element immersed interface methods, Preprint no. 2323, WIAS, Berlin, 2016.
    Abstract, PDF (1105 kByte)
    When solving elliptic partial differential equations in a region containing immersed interfaces (possibly evolving in time), it is often desirable to approximate the problem using a uniform background discretisation, not aligned with the interface itself. Optimal convergence rates are possible if the discretisation scheme is enriched by allowing the discrete solution to have jumps aligned with the surface, at the cost of a higher complexity in the implementation. A much simpler way to reformulate immersed interface problems consists in replacing the interface by a singular force field that produces the desired interface conditions, as done in immersed boundary methods. These methods are known to have inferior convergence properties, depending on the global regularity of the solution across the interface, when compared to enriched methods. In this work we prove that this detrimental effect on the convergence properties of the approximate solution is only a local phenomenon, restricted to a small neighbourhood of the interface. In particular we show that optimal approximations can be constructed in a natural and inexpensive way, simply by reformulating the problem in a distributionally consistent way, and by resorting to weighted norms when computing the global error of the approximation.

  • N. Ahmed, G. Matthies, Numerical studies of higher order variational time stepping schemes for evolutionary Navier--Stokes equations, Preprint no. 2322, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2322 .
    Abstract, PDF (1552 kByte)
    We present in this paper numerical studies of higher order variational time stepping schemes com-bined with finite element methods for simulations of the evolutionary Navier--Stokes equations. In particular, conforming inf-sup stable pairs of finite element spaces for approximating velocity and pressure are used as spatial discretization while continuous Galerkin--Petrov methods (cGP) and discontinuous Galerkin (dG) methods are applied as higher order variational time discretizations. Numerical results for the well-known problem of incompressible flows around a circle will be presented.

  • P.-É. Druet, Analysis of improved Nernst--Planck--Poisson models of isothermal compressible electrolytes subject to chemical reactions: The case of a degenerate mobility matrix, Preprint no. 2321, WIAS, Berlin, 2016.
    Abstract, PDF (387 kByte)
    We continue our investigations of the improved Nernst-Planck-Poisson model introduced by Dreyer, Guhlke and Müller 2013. In the paper by Dreyer, Druet, Gajewski and Guhlke 2016, the analysis relies on the hypothesis that the mobility matrix has maximal rank under the constraint of mass conservation (rank N-1 for the mixture of N species). In this paper we allow for the case that the positive eigenvalues of the mobility matrix tend to zero along with the partial mass densities of certain species. In this approach the mobility matrix has a variable rank between zero and N-1 according to the number of locally available species. We set up a concept of weak solution able to deal with this scenario, showing in particular how to extend the fundamental notion of emphdifferences of chemical potentials that supports the modelling and the analysis in Dreyer, Druet, Gajewski and Guhlke 2016. We prove the global-in-time existence in this solution class.

  • M. Hintermüller, M. Hinze, Ch. Kahle, T. Keil, A goal-oriented dual-weighted adaptive finite element approach for the optimal control of a nonsmooth Cahn--Hilliard--Navier--Stokes system, Preprint no. 2311, WIAS, Berlin, 2016.
    Abstract, PDF (640 kByte)
    This paper is concerned with the development and implementation of an adaptive solution algorithm for the optimal control of a time-discrete Cahn--Hilliard--Navier--Stokes system with variable densities. The free energy density associated to the Cahn--Hilliard system incorporates the double-obstacle potential which yields an optimal control problem for a family of coupled systems in each time instant of a variational inequality of fourth order and the Navier--Stokes equation. A dual-weighed residual approach for goal-oriented adaptive finite elements is presented which is based on the concept of C-stationarity. The overall error representation depends on primal residual weighted by approximate dual quantities and vice versa as well as various complementary mismatch errors. Details on the numerical realization of the adaptive concept and a report on numerical tests are given.

  • M. Kantner, Th. Koprucki, Numerical simulation of carrier transport in semiconductor devices at cryogenic temperatures, Preprint no. 2296, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2296 .
    Abstract, PDF (1445 kByte)
    At cryogenic temperatures the electron-hole plasma in semiconductor materials becomes strongly degenerate, leading to very sharp internal layers, extreme depletion in intrinsic domains and strong nonlinear diffusion. As a result, the numerical simulation of the drift-diffusion system suffers from serious convergence issues using standard methods. We consider a one-dimensional p-i-n diode to illustrate these problems and present a simple temperature-embedding scheme to enable the numerical simulation at cryogenic temperatures. The method is suitable for forward-biased devices as they appear e.g. in optoelectronic applications.

  • W. Dreyer, P.-É. Druet, P. Gajewski, C. Guhlke, Existence of weak solutions for improved Nernst--Planck--Poisson models of compressible reacting electrolytes, Preprint no. 2291, WIAS, Berlin, 2016.
    Abstract, PDF (638 kByte)

    We consider an improved Nernst-Planck-Poisson model for compressible electrolytes first proposed by Dreyer et al. in 2013. The model takes into account the elastic deformation of the medium. In particular, large pressure contributions near electrochemical interfaces induce an inherent coupling of mass and momentum transport. The model consists of convection-diffusion-reaction equations for the constituents of the mixture, of the Navier-Stokes equation for the barycentric velocity and the Poisson equation for the electrical potential. Cross-diffusion phenomena occur due to the principle of mass conservation. Moreover, the diffusion matrix (mobility matrix) has a zero eigenvalue, meaning that the system is degenerate parabolic. In this paper we establish the existence of a global-in- time weak solution for the full model, allowing for cross-diffusion and an arbitrary number of chemical reactions in the bulk and on the active boundary.
  • J. Haskovec, S. Hittmeir, P. Markowich, A. Mielke, Decay to equilibrium for energy-reaction-diffusion systems, Preprint no. 2233, WIAS, Berlin, 2016.
    Abstract, PDF (436 kByte)
    We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitely calculable constants and establish the convergence to thermodynamical equilibrium, at first in entropy and further in L1 using Cziszar-Kullback-Pinsker type inequalities.

  • CH. Heinemann, K. Sturm, Shape optimisation for a class of semilinear variational inequalities with applications to damage models, Preprint no. 2209, WIAS, Berlin, 2016.
    Abstract, PDF (590 kByte)
    The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an abstract operator setting where the operators are defined on polyhedral subsets of reflexive Banach spaces. The results are then refined for variational inequalities arising from minimisation problems for certain convex energy functionals considered over upper obstacle sets in $H^1$. One particularity is that we allow for dynamic obstacle functions which may arise from another optimisation problems. We prove a strong convergence property for the material derivative and establish state-shape derivatives under regularity assumptions. Finally, as a concrete application from continuum mechanics, we show how the dynamic obstacle case can be used to treat shape optimisation problems for time-discretised brittle damage models for elastic solids. We derive a necessary optimality system for optimal shapes whose state variables approximate desired damage patterns and/or displacement fields.

  • W. Dreyer, C. Guhlke, M. Landstorfer, R. Müller, New insights on the interfacial tension of electrochemical interfaces and the Lippmann equation, Preprint no. 2201, WIAS, Berlin, 2015.
    Abstract, PDF (4623 kByte)
    The Lippmann equation is considered as universal relationship between interfacial tension, double layer charge, and cell potential. Based on the framework of continuum thermo-electrodynamics we provide some crucial new insights to this relation. In a previous work we have derived a general thermodynamic consistent model for electrochemical interfaces, which showed a remarkable agreement to single crystal experimental data. Here we apply the model to a curved liquid metal electrode. If the electrode radius is large compared to the Debye length, we apply asymptotic analysis methods and obtain the Lippmann equation. We give precise definitions of the involved quantities and show that the interfacial tension of the Lippmann equation is composed of the surface tension of our general model, and contributions arising from the adjacent space charge layers. This finding is confirmed by a comparison of our model to experimental data of several mercury-electrolyte interfaces. We obtain qualitative and quantitative agreement in the 2V potential range for various salt concentrations. We also discuss the validity of our asymptotic model when the electrode curvature radius is comparable to the Debye length.

  • T. Ahnert, A. Münch, B. Niethammer, B. Wagner, Stability of concentrated suspensions under Couette and Poiseuille flow, Preprint no. 2159, WIAS, Berlin, 2015.
    Abstract, PDF (678 kByte)
    The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. Linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of two-dimensional Poiseuille flow gives rise to base state solutions that exhibit a jammed and unyielded region, due to shear-induced migration, as the maximum packing fraction is approached. The stability characteristics of the resulting Bingham-type flow is investigated and connections to the stability problem for the related classical Bingham-flow problem are discussed.

  Talks, Poster

  • A. Alphonse, A coupled bulk-surface reaction-diffusion system on a moving domain, Workshop ``Emerging Developments in Interfaces and Free Boundaries'', January 23 - 28, 2017, Mathematisches Forschungszentrum Oberwolfach, January 25, 2017.

  • M. Heida, On G-convergence and stochastic two-scale convergences of the squareroot approximation scheme to the Fokker--Planck operator, GAMM-Workshop on Analysis of Partial Differential Equations, September 27 - 29, 2017, Eindhoven University of Technology, Mathematics and Computer Science Department, Netherlands, September 28, 2017.

  • M. Kantner, Hybrid quantum-classical modeling of electrically driven quantum light sources, Meeting of the MATHEON Scientific Advisory Board 2017, TU Berlin, Institut für Mathematik, November 13, 2017.

  • M. Kantner, Simulations of quantum dot devices by coupling of quantum master equations and semi-classical transport theory, 17th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD2017), July 24 - 28, 2017, Technical University of Denmark, Copenhagen, July 27, 2017.

  • M. Liero, Modeling and simulation of electrothermal feedback in large-area organic LEDs, Numerical Simulation of Optoelectronic Devices (NUSOD 2017), session ``Light-Emitting Diodes'', July 24 - 28, 2017, Technical University of Denmark, Lyngby Campus, Kopenhagen, Denmark, July 25, 2017.

  • CH. Merdon, A novel concept for the discretisation of the coupled Nernst--Planck--Poisson--Navier--Stokes system, 14th Symposium on Fuel Cell Modelling and Experimental Validation (MODVAL 14), March 2 - 3, 2017, Karlsruher Institut für Technologie, Institut für Angewandte Materialien, Karlsruhe, Germany, March 3, 2017.

  • CH. Merdon, Druckrobuste Finite-Elemente-Methoden für die Navier-Stokes-Gleichungen, Universität Paderborn, Institut für Mathematik, April 25, 2017.

  • CH. Merdon, Pressure-robustness in mixed finite element discretisations for the Navier--Stokes equations, Universität des Saarlandes, Fakultät für Mathematik und Informatik, July 12, 2017.

  • D. Peschka, Doping optimization for optoelectronic devices, Numerical Simulation of Optoelectronic Devices (NUSOD 2017), Post-Deadline session, July 27 - 28, 2017, Technical University, Lyngby Campus, Kopenhagen, Denmark, July 28, 2017.

  • D. Peschka, Motion of thin droplets over surfaces, Making a Splash -- Driplets, Jets and Other Singularities, March 20 - 24, 2017, Brown University, Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, USA, March 22, 2017.

  • D. Peschka, Variational structure of fluid motion with contact lines in thin-film models, Kolloquium Angewandte Mathematik, Universität der Bundeswehr, München, May 31, 2017.

  • N. Ahmed, Higher-order discontinuous Galerkin time discretizations for the evolutionary Navier--Stokes equations, Technische Universität Dresden, Institut für Numerische Mathematik, March 9, 2017.

  • N. Ahmed, On really locking-free mixed finite element methods for the transient incompressible Stokes equations, CASM International Conference on Applied Mathematics, May 22 - 24, 2017, Lahore University of Management Sciences, Centre for Advanced Studies in Mathematics, Pakistan, May 22, 2017.

  • C. Bartsch, ParMooN -- A parallel finite element solver, Part I, Indian Institute of Science, Supercomputer Education and Research Centre, Bangalore, India, March 16, 2017.

  • A. Caiazzo, Estimation of cardiovascular system parameters from real data, 2nd Leibniz MMS Days 2017, February 22 - 23, 2017, Technische Informationsbibliothek, Hannover, February 22, 2017.

  • A. Caiazzo, Homogenization methods for weakly compressible elastic materials forward and inverse problem, Workshop on Numerical Inverse and Stochastic Homogenization, February 13 - 17, 2017, Universität Bonn, Hausdorff Research Institute for Mathematics, February 17, 2017.

  • P.-É. Druet, Analysis of recent Nernst--Planck--Poisson--Navier--Stokes systems of electrolytes, 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2017), Section S14 ``Applied Analysis'', March 6 - 10, 2017, Bauhaus Universität Weimar/Technische Universität Ilmenau, Weimar, March 7, 2017.

  • P.-É. Druet, Existence of weak solutions for improved Nernst--Planck--Poisson models of compressible electrolytes, Seminar EDE, Institute of Mathematics, Department of Evolution Differential Equations (EDE), Prague, Czech Republic, January 10, 2017.

  • P. Friz, Geometric aspects in pathwise stochastic analysis, High Risk High Gain - Groundbreaking Research in Berlin, August 31 - September 3, 2017, Technische Universität Berlin, Stabsstelle Presse, September 2, 2017.

  • M. Hintermüller, Generalized Nash equilibrium problems in Banach spaces: Theory, Nikaido--Isoda-based path-following methods, and applications, The Third International Conference on Engineering and Computational Mathematics (ECM2017), Stream 3 ``Computational Optimization'', May 31 - June 2, 2017, The Hong Kong Polytechnic University, China, June 2, 2017.

  • M. Hintermüller, Non-smooth structures in PDE-constrained optimization, Mathematisches Kolloquium, Universität Duisburg-Essen, Fakultät für Mathematik, Essen, January 11, 2017.

  • M. Hintermüller, Recent trends in PDE-constrained optimization with non-smooth structures, Fourth Conference on Numerical Analysis and Optimization (NAOIV-2017), January 2 - 5, 2017, Sultan Qaboos University, Muscat, Oman, January 4, 2017.

  • TH. Koprucki, Comparison of consistent flux discretizations for drift diffusion beyond Boltzmann statistics, Numerical Simulation of Optoelectronic Devices (NUSOD 2017), session ``Numerical Methods'', July 24 - 28, 2017, Technical University of Denmark, Lyngby Campus, Kopenhagen, Denmark, July 27, 2017.

  • TH. Koprucki, Mathematical models as research data in numerical simulation of opto-electronic devices, Numerical Simulation of Optoelectronic Devices (NUSOD 2017), session ``Model Representation'', July 24 - 28, 2017, Technical University of Denmark, Lyngby Campus, Kopenhagen, Denmark, July 27, 2017.

  • CH. Merdon, Pressure-robust finite element methods for the Navier--Stokes equations, GAMM Workshop on Numerical Analysis, November 1 - 2, 2017, Rheinisch-Westfälische Technische Hochschule Aachen, November 2, 2017.

  • CH. Merdon, Pressure-robust mixed finite element methods for the Navier--Stokes equations, scMatheon Workshop RMMM 8 - Berlin 2017, Reliable Methods of Mathematical Modeling, July 31 - August 3, 2017, Humboldt-Universität zu Berlin, August 2, 2017.

  • A. Mielke, Mathematical modeling of semiconductors: From quantum mechanics to devices, CIM-WIAS Workshop ``Topics in Applied Analysis and Optimisation'', December 6 - 8, 2017, Centro de Matemática, Lisboa, Portugal, December 8, 2017.

  • U. Wilbrandt, ParMooN -- A parallel finite element solver, Part II, Indian Institute of Science, Supercomputer Education and Research Centre, Bangalore, India, March 16, 2017.

  • K. Disser, Convergence for gradient systems of slow and fast chemical reactions, Joint Annual Meeting of DMV and GAMM, Session ``Applied Analysis'', March 7 - 11, 2016, Technische Universität Braunschweig, Braunschweig, March 11, 2016.

  • M. Kantner, Multi-scale modeling and numerical simulation of single-photon emitters, Matheon Workshop--9th Annual Meeting ``Photonic Devices", Zuse Institut, Berlin, March 3, 2016.

  • M. Kantner, Multi-scale modelling and simulation of single-photon sources on a device level, Euro--TMCS II Theory, Modelling & Computational Methods for Semiconductors, Tyndall National Institute and University College Cork, Cork, Ireland, December 9, 2016.

  • M. Liero, On $p(x)$-Laplace thermistor models describing eletrothermal feedback in organic semiconductors, The 19th European Conference on Mathematics for Industry (ECMI 2016), Minisymposium 23 ``Charge Transport in Semiconductor Materials: Emerging and Established Mathematical Topics'', June 13 - 17, 2016, Universidade de Santiago de Compostela, Spain, June 15, 2016.

  • M. Liero, On electrothermal feedback in organic light-emitting diodes, Berlin Dresden Prague Würzburg Workshop ``Mathematics of Continuum Mechanics'', Technische Universität Dresden, Fachbereich Mathematik, December 5, 2016.

  • CH. Merdon, J. Fuhrmann, A. Linke, A.A. Abd-El-Latif, M. Khodayari, P. Reinsberg, H. Baltruschat, Inverse modelling of thin layer flow cells and RRDEs, The 67th Annual Meeting of the International Society of Electrochemistry, Den Haag, Netherlands, August 21 - 26, 2016.

  • R. Müller, W. Dreyer, J. Fuhrmann, C. Guhlke, New insights into Butler--Volmer kinetics from thermodynamic modeling, The 67th Annual Meeting of the International Society of Electrochemistry, Den Haag, Netherlands, August 21 - 26, 2016.

  • D. Peschka, Multi-phase flows with contact lines: Solid vs liquid substrates, Industrial and Applied Mathematics Seminar, University of Oxford, Mathematical Institute, UK, October 27, 2016.

  • D. Peschka, Thin film free boundary problems --- Modeling of contact line dynamics with gradient formulations, CeNoS-Kolloquium, Westfälische Wilhelms-Universität Münster, Center for Nonlinear Science, January 12, 2016.

  • M. Thomas, Analysis and optimization for edge-emitting semiconductor heterostructures, 7th European Congress of Mathematics (ECM), session CS-8-A, July 18 - 22, 2016, Technische Universität Berlin, Berlin, July 19, 2016.

  • M. Thomas, Analysis and optimization for edge-emitting semiconductor heterostructures, The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session 2 ``Emergence and Dynamics of Patterns in Nonlinear Partial Differential Equation'', July 1 - 5, 2016, The American Institute of Mathematical Sciences, Orlando (Florida), USA, July 3, 2016.

  • M. Thomas, Non-smooth PDEs in material failure: Towards dynamic fracture, Joint Annual Meeting of DMV and GAMM, Section 14 ``Applied Analysis'', March 7 - 11, 2016, Technische Universität Braunschweig, March 10, 2016.

  • N. Ahmed, A review of VMS methods for the simulation of turbulent incompressible flows, International Conference on Differential Equations and Applications, May 26 - 28, 2016, Lahore University of Management Sciences, Pakistan, May 27, 2016.

  • N. Ahmed, On the grad-div stabilization for the steady Oseen and Navier--Stokes evaluations, International Conference of Boundary and Interior Layers (BAIL 2016), August 15 - 19, 2016, Beijing Computational Science Research Center, Beijing, China, August 15, 2016.

  • A. Caiazzo, A comparative study of backflow stabilization methods, 7th European Congress of Mathematics (7ECM), July 18 - 22, 2016, Technische Universität Berlin, Berlin, July 19, 2016.

  • A. Caiazzo, Backflow stabilization methods for open boundaries, Christian-Albrechts-Universität zu Kiel, Angewandte Mathematik, Kiel, May 19, 2016.

  • D.H. Doan, Numerical methods in non-Boltzmann regimes, sc Matheon Workshop, 9th Annual Meeting ``Photonic Devices'', March 3 - 4, 2016, Zuse Institute Berlin, Berlin, March 4, 2016.

  • P.-É. Druet, Existence of global weak solutions for generalized Poisson--Nernst--Planck systems, 7th European Congress of Mathematics (ECM), minisymposium ``Analysis of Thermodynamically Consistent Models of Electrolytes in the Context of Battery Research'', July 18 - 22, 2016, Technische Universität Berlin, Berlin, July 20, 2016.

  • P. Farrell, Scharfetter--Gummel schemes for Non-Boltzmann statistics, Conference on Scientific Computing (ALGORITMY 2016), March 14 - 18, 2016, Slovak University of Technology, Department of Mathematics and Descriptive Geometry, Podbanské, Slovakia, March 17, 2016.

  • P. Farrell, Scharfetter--Gummel schemes for non-Boltzmann statistics, The 19th European Conference on Mathematics for Industry (ECMI2016), Minisymposium 23 ``Charge Transport in Semiconductor Materials: Emerging and Established Mathematical Topics'', June 13 - 17, 2016, Universidade de Santiago de Compostela, Spain, June 14, 2016.

  • J. Fuhrmann, Ch. Merdon, A thermodynamically consistent numerical approach to Nernst--Planck--Poisson systems with volume constraints, The 67th Annual Meeting of the International Society of Electrochemistry, Den Haag, Netherlands, August 21 - 26, 2016.

  • J. Fuhrmann, W. Dreyer, C. Guhlke, M. Landstorfer, R. Müller, A. Linke, Ch. Merdon, Modeling and numerics for electrochemical systems, Micro Battery and Capacitive Energy Harvesting Materials -- Results of the MatFlexEnd Project, Universität Wien, Austria, September 19, 2016.

  • J. Fuhrmann, A. Linke, Ch. Merdon, M. Khodayari , H. Baltruschat, Detection of solubility, transport and reaction coefficients from experimental data by inverse modelling of thin layer flow cells, 1st Leibniz MMS Mini Workshop on CFD & GFD, WIAS Berlin, September 8 - 9, 2016.

  • J. Fuhrmann, A. Linke, Ch. Merdon, W. Dreyer, C. Guhle, M. Landstorfer, R. Müller, Numerical methods for electrochemical systems, 2nd Graz Battery Days, Graz, Austria, September 27 - 28, 2016.

  • C. Guhlke, J. Fuhrmann, W. Dreyer, R. Müller, M. Landstorfer, Modeling of batteries, Batterieforum Deutschland 2016, Berlin, April 6 - 8, 2016.

  • M. Hintermüller, Adaptive finite elements in total variation based image denoising, SIAM Conference on Imaging Science, Minisymposium ``Leveraging Ideas from Imaging Science in PDE-constrained Optimization'', May 23 - 26, 2016, Albuquerque, USA, May 24, 2016.

  • M. Hintermüller, Nonsmooth structures in PDE constrained optimization, 66th Workshop ``Advances in Convex Analysis and Optimization'', July 5 - 10, 2016, International Centre for Scientific Culture ``E. Majorana'', School of Mathematics ``G. Stampacchia'', Erice, Italy, July 9, 2016.

  • M. Hintermüller, Optimal control of multiphase fluids and droplets, WIAS-PGMO Workshop on Nonsmooth and Stochastic Optimization with Applications to Energy Management, May 10 - 12, 2016, WIAS Berlin, May 11, 2016.

  • M. Hintermüller, Optimal control of multiphase fluids and droplets, The Fifth International Conference on Continuous Optimization, Session: ``Recent Developments in PDE-constrained Optimization I'', August 6 - 11, 2016, Tokyo, Japan, August 10, 2016.

  • M. Hintermüller, Optimal control of multiphase fluids and droplets, Salzburg Mathematics Colloquium, Universität Salzburg, Fachbereich Mathematik, Austria, June 9, 2016.

  • M. Hintermüller, Optimal selection of the regularisation function in a localised TV model, SIAM Conference on Imaging Science, Minisymposium ``Analysis and Parameterisation of Derivative Based Regularisation'', May 23 - 26, 2016, Albuquerque, USA, May 24, 2016.

  • V. John, Analytical and numerical results for algebraic flux correction schemes, Conference on Recent Advances in Analysis and Numerics of Hyperbolic Conservation Laws, September 8 - 10, 2016, Otto-von-Guericke Universität Magdeburg, September 9, 2016.

  • A. Mielke, Entropy-entropy production estimates for energy-reaction diffusion systems, Workshop ``Forefront of PDEs: Modelling, Analysis and Numerics'', December 12 - 14, 2016, Technische Universität Wien, Institut für Analysis and Scientific Computing, Austria, December 13, 2016.

  • A. Mielke, Evolution driven by energy and entropy, SFB1114 Kolloquium, Freie Universität Berlin, Berlin, June 30, 2016.

  • A.G. Vladimirov, Interaction of temporal cavity solitons in driven fiber resonators and mode-locked lasers, International Tandem Workshop on Pattern Dynamics in Nonlinear Optical Cavities, August 15 - 19, 2016, Max-Planck-Institut für Physik komplexer Systeme, Dresden, August 15, 2016.

  • K. Disser, Asymptotic behavior of a rigid body with a cavity filled by a viscous liquid, Mathematical Thermodynamics of Complex Fluids, June 29 - July 3, 2015, Centro Internazionale Matematico Estivo (CIME), Cetraro, Italy, June 30, 2015.

  • K. Disser, Asymptotic behavior of a rigid body with a cavity filled by a viscous liquid, Workshop ``Young Researchers in Fluid Dynamics'', June 18 - 19, 2015, Technische Universität Darmstadt, Fachbereich Mathematik, Darmstadt, June 18, 2015.

  • K. Disser, Asymptotic behavior of a rigid body with a cavity filled by a viscous liquid, Seminar ``Dynamische Systeme'', Technische Universität München, Zentrum Mathematik, München, February 2, 2015.

  • K. Disser, Asymptotic behavior of a rigid body with a cavity filled by a viscous liquid, Oberseminar ``Analysis'', Universität Kassel, Institut für Mathematik, Kassel, January 12, 2015.

  • K. Disser, Dynamik von Starrkörpern, die mit einer Flüssigkeit gefüllt sind, und das Ei-Problem, Mathematisches Kolloquium, Heinrich-Heine Universität Düsseldorf, Institut für Mathematik, Düsseldorf, April 10, 2015.

  • N. Rotundo, Analytical methods for doping optimization for semiconductor devices, Minisymposium ``Numerical and Analytical Aspects in Semiconductor Theory'' of the 8th International Congress on Industrial and Applied Mathematics (ICIAM 2015), August 10 - 14, 2015, International Council for Industrial and Applied Mathematics, Beijing, China, August 10, 2015.

  • M. Heida, Modeling of fluid interfaces, Jahrestagung der Deutschen Mathematiker-Vereinigung, Minisymposium ``Mathematics of Fluid Interfaces'', September 21 - 25, 2015, Universität Hamburg, Fakultät für Mathematik, Informatik und Naturwissenschaften, Hamburg, September 23, 2015.

  • CH. Heinemann, Damage processes in thermoviscoelastic materials with damage-dependent thermal expansion coefficients, 3rd Workshop of the GAMM Activity Group Analysis of Partial differential Equations, September 30 - October 2, 2015, Universität Kassel, Institut für Mathematik, October 1, 2015.

  • CH. Heinemann, On elastic Cahn--Hilliard systems coupled with evolution inclusions for damage processes, 86th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2015), Young Researchers' Minisymposium 2, March 23 - 27, 2015, Lecce, Italy, March 23, 2015.

  • M. Landstorfer, Theory, structure and experimental justification of the metal/electrolyte interface, Minisymposium `` Recent Developments on Electrochemical Interface Modeling'' of the 8th International Congress on Industrial and Applied Mathematics (ICIAM 2015), August 10 - 14, 2015, International Council for Industrial and Applied Mathematics, Beijing, China, August 11, 2015.

  • M. Liero, Electrothermal modeling of large-area OLEDs, sc Matheon Center Days, April 20 - 21, 2015, Technische Universität Berlin, Institut für Mathematik, Berlin, April 20, 2015.

  • M. Liero, OLEDs -- eine heiße Sache?, Organische Leuchtdioden, Workshop im Handlungsfeld Lichttechnik, OpTec Berlin Brandenburg e.V., Berlin, May 18, 2015.

  • M. Liero, On a PDE thermistor system for large-area OLEDs, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2015), March 11 - 13, 2015, WIAS Berlin, Berlin, March 12, 2015.

  • CH. Merdon, Inverse modeling of thin layer flow cells for detection of solubility transport and reaction coefficients from experimental data, 17th Topical Meeting of the International Society of Electrochemistry Multiscale Analysis of Electrochemical Systems, May 31 - June 3, 2015, Saint Malo Congress Center, France, June 1, 2015.

  • D. Peschka, Mathematical modeling, analysis, and optimization of strained germanium-microbridges, sc Matheon Center Days, April 20 - 21, 2015, Technische Universität Berlin, Institut für Mathematik, Berlin, April 20, 2015.

  • D. Peschka, Numerics of contact line motion for thin films, MATHMOD 2015, Minisymposium ``Free Boundary Problems in Applications: Recent Advances in Modelling, Simulation and Optimization'', February 17 - 20, 2015, Technische Universität Wien, Institut für Analysis und Scientific Computing, Wien, Austria, February 19, 2015.

  • D. Puzyrev, Delay induced multistability and wiggling movement of laser cavity solitons, International Workshop ``Waves, Solitons and Turbulence in Optical Systems'' (WASTOS15), Berlin, October 12 - 14, 2015.

  • A. Glitzky, Finite volume discretized reaction-diffusion systems in heterostructures, Conference on Partial Differential Equations, March 25 - 29, 2015, Technische Universität München, Zentrum Mathematik, München, March 28, 2015.

  • M. Thomas, Analysis for edge-emitting semiconductor heterostructures, Minisymposium ``Numerical and Analytical Aspects in Semiconductor Theory'' of the 8th International Congress on Industrial and Applied Mathematics (ICIAM 2015), August 10 - 14, 2015, International Council for Industrial and Applied Mathematics, Beijing, China, August 10, 2015.

  • M. Thomas, Analysis of nonsmooth PDE systems with application to material failure---towards dynamic fracture, Minisymposium ``Analysis of Nonsmooth PDE Systems with Application to Material Failure'' of the 8th International Congress on Industrial and Applied Mathematics (ICIAM 2015), August 10 - 14, 2015, International Council for Industrial and Applied Mathematics, Beijing, China, August 12, 2015.

  • M. Thomas, Coupling rate-independent and rate-dependent processes: Existence results, Applied Mathematics Seminar, Università di Pavia, Dipartimento di Matematica, Pavia, Italy, March 5, 2015.

  • M. Thomas, Coupling rate-independent and rate-dependent processes: Evolutionary Gamma-convergence results, 86th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2015), Session on Applied Analysis, March 23 - 27, 2015, Università del Salento, Lecce, Italy, March 26, 2015.

  • M. Thomas, Coupling rate-independent and rate-dependent processes: Existence and evolutionary Gamma convergence, INdAM Workshop ``Special Materials in Complex Systems -- SMaCS 2015'', May 18 - 22, 2015, Rome, Italy, May 19, 2015.

  • M. Thomas, Coupling rate-independent and rate-dependent processes: Existence results, 86th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2015), GAMM Juniors Poster Session, Lecce, Italy, March 23 - 27, 2015.

  • M. Thomas, Modeling of edge-emitting lasers based on tensile strained germanium microstripes, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2015), March 11 - 13, 2015, WIAS Berlin, Berlin, March 11, 2015.

  • N. Ahmed, Adaptive time step control with variational time stepping schemes for convection-diffusion-reaction equations, 26th Biennial Numerical Analysis Conference, June 23 - 26, 2015, University of Strathclyde, Glasgow, UK, June 23, 2015.

  • N. Ahmed, Higher order time stepping schemes, 13th European Finite Element Fair, June 5 - 6, 2015, Charles University in Prague, Praha, Czech Republic, June 5, 2015.

  • A. Caiazzo, A Stokes-residual based backflow stabilization for incompressible flows, XXIV Congreso de Ecuaciones Diferenciales y Aplicaciones, June 8 - 12, 2015, Universidad de Cádiz, Cádiz, Spain, June 10, 2015.

  • A. Caiazzo, Modeling and simulation of fluid flows through a porous interface, Besançon Week on Numerical Analysis: XFEM, Nitsche FEM, Adaptive FEM, Artificial Boundary Conditions, June 15 - 21, 2015, Université de Franche Comté, Besançon, France, June 19, 2015.

  • A. Caiazzo, Multiscale modeling of weakly compressible elastic materials, Workshop on Aktive Drag Reduction, November 9 - 10, 2015, Rheinisch-Westfälische Technische Hochschule Aachen, Institut für Geometrie und Praktische Mathematik, Aachen, November 10, 2015.

  • A. Caiazzo, Multiscale modeling of weakly compressible elastic materials in harmonic regime, Rheinische Friedrich-Wilhelms-Universität Bonn, Institut für Numerische Simulation, Bonn, May 21, 2015.

  • A.G. Vladimirov, Application of delay differential equations to the analysis of nonlinear dynamics in mode-locked lasers, Colloquium Nonlinear Sciences, Universität Münster, Center for Nonlinear Sciences, May 19, 2015.

  • A.G. Vladimirov, Feedback induced instabilities of cavity solitons, International Symposium on Physics and Applications of Laser Dynamics 2015, November 4 - 6, 2015, CentraleSupélec, Metz, France, November 6, 2015.

  • K. Disser, Asymptotic behaviour of a rigid body with a cavity filled by a viscous liquid, Second Workshop of the GAMM Activity Group on "Analysis of Partial Differential Equations", September 29 - October 1, 2014, Universität Stuttgart, Lehrstuhl für Analysis und Modellierung, October 1, 2014.

  • K. Disser, Asymptotic behaviour of a rigid body with a cavity filled by a viscous liquid, Autumn School and Workshop on Mathematical Fluid Dynamics, October 27 - 30, 2014, Universität Darmstadt, International Research Training Group 1529, Bad Boll, October 28, 2014.

  • S. Heinz, Analysis and numerics of a phase-transformation model, 13th GAMM Seminar on Microstructures, January 17 - 18, 2014, Ruhr-Universität Bochum, Lehrstuhl für Mechanik - Materialtheorie, January 18, 2014.

  • TH. Koprucki, DeviceSimulation: Mathematische Fragestellungen und Numerik, Block-Seminar des SFB 787 ``Nanophotonik'', May 21 - 23, 2014, Technische Universität Berlin, Graal-Müritz, May 23, 2014.

  • TH. Koprucki, On modifications of the Scharfetter--Gummel scheme for drift-diffusion equations with Fermi-like statistical distribution functions, 14th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2014), September 1 - 5, 2014, Palma de Mallorca, Spain, September 3, 2014.

  • M. Liero, Electrothermical modeling of large-area OLEDs, Kick-Off Meeting of the ECMI Special Interest Group ``Sustainable Energy'' on Nanostructures for Photovoltaics and Energy Storage, December 8 - 9, 2014, Technische Universität Berlin, Institut für Mathematik, December 8, 2014.

  • A. Linke, Ch. Merdon, Optimal and pressure-independent $L^2$ velocity error estimates for a modified Crouzeix--Raviart element with BDM reconstructions, The International Symposium of Finite Volumes for Complex Applications VII (FVCA 7), Berlin-Brandenburgische Akademie der Wissenschaften, June 15 - 20, 2014.

  • A. Linke, Ein neues Konstruktionsprinzip zur divergenzfreien Diskretisierung der inkompressiblen Navier-Stokes-Gleichungen, Ruhr-Universität Bochum, Fakultät für Mathematik, July 17, 2014.

  • A. Linke, On the role of the Helmholtz decomposition in incompressible flows and a new variational crime, NonLinear PDE and Applications: Theoretical and Numerical Study, May 5 - 7, 2014, Abdelmalek Essadi University, Tanger, Morocco, May 6, 2014.

  • A. Linke, On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime, Technische Universität Wien, Institut für Analysis und Scientific Computing, Austria, April 2, 2014.

  • A. Linke, On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime, Technische Universität Hamburg-Harburg, Institut für Mathematik, January 7, 2014.

  • A. Linke, On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime, Friedrich-Alexander-Universität Erlangen-Nürnberg, Fachbereich Mathematik, November 20, 2014.

  • A. Linke, On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime, Georg-August-Universität Göttingen, Institut für Numerische und Angewandte Mathematik, December 9, 2014.

  • M. Radziunas, Effective numerical algorithm for simulations of broad area semiconductor lasers, "International Workshop on Application of Parallel Computation in Industry and Engeneering (APCIE) in conjunction with EURO-PAR' 2014'', August 25 - 26, 2014, Porto, Portugal, August 25, 2014.

  • A. Glitzky, Drift-diffusion models for heterostructures in photovoltaics, 8th European Conference on Elliptic and Parabolic Problems, Minisymposium ``Qualitative Properties of Nonlinear Elliptic and Parabolic Equations'', May 26 - 30, 2014, Universität Zürich, Institut für Mathematik, organized in Gaeta, Italy, May 27, 2014.

  • M. Thomas, Existence & stability results for rate-independent processes in viscoelastic materials, Applied Mathematics Seminar, Università di Pavia, Dipartimento di Matematica, Italy, March 18, 2014.

  • M. Thomas, Existence and stability results for rate-independent processes in viscoelastic materials, Women in Partial Differential Equations & Calculus of Variations Workshop, March 6 - 8, 2014, University of Oxford, Mathematical Institute, UK, March 6, 2014.

  • M. Thomas, GENERIC for solids with dissipative interface processes, 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2014), GAMM Juniors' Poster Session, Friedrich-Alexander Universität Erlangen-Nürnberg, March 10 - 14, 2014.

  • M. Thomas, Rate-independent systems with viscosity and inertia: Existence and evolutionary Gamma-convergence, Workshop ``Variational Methods for Evolution'', December 14 - 20, 2014, Mathematisches Forschungsinstitut Oberwolfach, December 18, 2014.

  • M. Thomas, Rate-independent, partial damage in thermo-viscoelastic materials, 7th International Workshop on Multi-Rate Processes & Hysteresis, 2nd International Workshop on Hysteresis and Slow-Fast Systems (MURPHYS-HSFS-2014), April 7 - 11, 2014, WIAS Berlin, April 8, 2014.

  • M. Thomas, Rate-independent, partial damage in thermo-viscoelastic materials with inertia, International Workshop ``Variational Modeling in Solid Mechanics'', September 22 - 24, 2014, University of Udine, Department of Mathematics and Informatics, Italy, September 23, 2014.

  • M. Thomas, Rate-independent, partial damage in thermo-viscoelastic materials with inertia, Oberseminar ``Analysis und Angewandte Mathematik'', Universität Kassel, Institut für Mathematik, December 1, 2014.

  • M. Thomas, Stress-driven local-solution approach to quasistatic brittle delamination, 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2014), Session on Applied Analysis, March 10 - 14, 2014, Friedrich-Alexander Universität Erlangen-Nürnberg, March 11, 2014.

  • M. Thomas, Thermomechanical modeling of dissipative processes in elastic media via energy and entropy, The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session 8: Emergence and Dynamics of Patterns in Nonlinear Partial Differential Equations from Mathematical Science, July 7 - 11, 2014, Madrid, Spain, July 8, 2014.

  • A. Caiazzo, Effcient blood flow simulations for the design of stented valve size reducer in enlarged ventricular outflow tracts, 4th International Conference on Engineering Frontiers in Pediatric and Congenital Heart Disease, May 21 - 22, 2014, INRIA Research Centre Paris -- Rocquencourt, France, May 22, 2014.

  • A. Caiazzo, Stabilization at backflow, European Finite Element Fair, May 30 - 31, 2014, Universität Wien, Austria, May 30, 2014.

  • J. Fuhrmann, A. Linke, Ch. Merdon, M. Khodayari, H. Baltruschat, Detection of solubility, transport and reaction coefficients from experimental data by inverse modeling of thin layer flow cells, 65th Annual Meeting of the International Society of Electrochemistry, Lausanne, Switzerland, August 31 - September 5, 2014.

  • J. Fuhrmann, A. Linke, Ch. Merdon, Coupling of fluid flow and solute transport using a divergence-free reconstruction of the Crouzeix--Raviart element, The International Symposium of Finite Volumes for Complex Applications VII (FVCA 7), Berlin-Brandenburgische Akademie der Wissenschaften, June 15 - 20, 2014.

  • J. Fuhrmann, Ch. Merdon, Activity based finite volume methods for generalised Nernst--Planck--Poisson systems, 65th Annual Meeting of the International Society of Electrochemistry, Lausanne, Switzerland, August 31 - September 5, 2014.

  • J. Fuhrmann, Activity based finite volume methods for generalised Nernst--Planck--Poisson systems, The International Symposium of Finite Volumes for Complex Applications VII (FVCA 7), Berlin-Brandenburgische Akademie der Wissenschaften, June 15 - 20, 2014.

  • L. Kamenski, A study on the conditioning of finite element equations with general (anisotropic) meshes via a density function approach, 27th Chemnitz FEM Symposium, September 22 - 24, 2014, Technische Universität Chemnitz, September 24, 2014.

  • L. Kamenski, Hessian recovery and FE mesh adaptation, European Finite Element Fair, May 30 - 31, 2014, Universität Wien, Austria, May 31, 2014.

  • L. Kamenski, How a non-convergent Hessian recovery works in mesh adaptation, 2014 AARMS-CRM Workshop on Adaptive Methods for PDEs, August 17 - 22, 2014, Memorial University of Newfoundland, Canada, August 20, 2014.

  • A. Mielke, Gradient structures and dissipation distances for reaction-diffusion systems, Seminar ``Analysis of Fluids and Related Topics'', Princeton University, Department of Mechanical and Aerospace Engineering, Princeton, NJ, USA, March 6, 2014.

  • A. Mielke, How thermodynamics induces geometry structures for reaction-diffusion systems, Gemeinsames Mathematisches Kolloquium der Universitäten Gießen und Marburg, Universität Gießen, Mathematisches Institut, January 15, 2014.

  • A. Mielke, On gradient structures and dissipation distances for reaction-diffusion systems, Kolloquium ``Angewandte Mathematik'', Friedrich-Alexander-Universität Erlangen-Nürnberg, Department Mathematik, July 3, 2014.

  • A. Mielke, On gradient structures for reaction-diffusion systems, Joint Analysis Seminar, Rheinisch-Westfälische Technische Hochschule Aachen (RWTH), Institut für Mathematik, February 4, 2014.

  • S. Neukamm, Homogenization of nonlinear bending plates, Workshop ``Relaxation, Homogenization, and Dimensional Reduction in Hyperelasticity'', March 25 - 27, 2014, Université Paris-Nord, France, March 26, 2014.

  • H. Stephan, Inequalities for Markov operators and applications to forward and backward PDEs, The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session 88: Stochastic Processes and Spectral Theory for Partial Differential Equations and Boundary Value Problems, July 7 - 11, 2014, Madrid, Spain, July 8, 2014.

  • U. Wilbrandt, Iterative subdomain methods for Stokes--Darcy problems, Norddeutsches Kolloquium über Angewandte Analysis und Numerische Mathematik (NoKo), May 9 - 10, 2014, Christian-Albrechts-Universität zu Kiel, May 9, 2014.

  • TH. Koprucki, Generalization of the Scharfetter--Gummel scheme, Organic Photovoltaics Workshop 2013, December 10 - 11, 2013, University of Oxford, Mathematical Insitute, UK, December 10, 2013.

  • TH. Koprucki, Discretization scheme for drift-diffusion equations with a generalized Einstein relation, scshape Matheon Workshop ``6th Annual Meeting Photonic Devices'', February 21 - 22, 2013, Konrad-Zuse-Zentrum für Informationstechnik Berlin, February 22, 2013.

  • S. Neukamm, Quantitative results in stochastic homogenization, sc Matheon Multiscale Seminar, Technische Universität Berlin, Institut für Mathematik, June 27, 2013.

  • S. Neukamm, Quantitative results in stochastic homogenization, Oberseminar Analysis, Technische Universität Dresden, Fakultät Mathematik und Naturwissenschaften, June 13, 2013.

  • P.N. Racec, Wigner--Eisenbud problem within finite volume method: application to electronic transport in cylindrical nanowire heterostructures, QMATH12 -- Mathematical Results in Quantum Mechanics, September 10 - 13, 2013, Humboldt-Universität zu Berlin, Berlin, September 12, 2013.

  • A. Glitzky, Continuous and finite volume discretized reaction-diffusion systems in heterostructures, Asymptotic Behaviour of Systems of PDE Arising in Physics and Biology: Theoretical and Numerical Points of View, November 6 - 8, 2013, Lille 1 University -- Science and Technology, France, November 6, 2013.

  • D. Knees, Crack evolution models based on the Griffith criterion, Workshop on Mathematical Aspects of Continuum Mechanics, October 12 - 14, 2013, The Japan Society for Industrial and Applied Mathematics, Kanazawa, Japan, October 13, 2013.

  • D. Knees, Global spatial regularity for elasticity models with cracks and contact, Journées Singulières Augmentées 2013, August 26 - 30, 2013, Université de Rennes 1, France, August 27, 2013.

  • D. Knees, Global spatial regularity results for crack with contact and application to a fracture evolution model, Oberseminar Nichtlineare Analysis, Universität Köln, Mathematisches Institut, October 28, 2013.

  • D. Knees, Modeling and analysis of crack evolution based on the Griffith criterion, Nonlinear Analysis Seminar, Keio University of Science, Yokohama, Japan, October 9, 2013.

  • D. Knees, On energy release rates for nonlinearly elastic materials, Workshop on Mathematical Aspects of Continuum Mechanics, October 12 - 14, 2013, The Japan Society for Industrial and Applied Mathematics, Kanazawa, Japan, October 12, 2013.

  • D. Knees, Weak solutions for rate-independent systems illustrated at an example for crack propagation, BMS Intensive Course on Evolution Equations and their Applications, November 27 - 29, 2013, Technische Universität Berlin, Berlin Mathematical School, November 28, 2013.

  • M. Thomas, Local versus energetic solutions in rate-independent brittle delamination, DIMO2013 -- Diffuse Interface Models, September 10 - 13, 2013, Levico Terme, Italy, September 13, 2013.

  • M. Thomas, A stress-driven local solution approach to quasistatic brittle delamination, BMS Intensive Course on Evolution Equations and their Applications, November 27 - 29, 2013, Technische Universität Berlin, Berlin Mathematical School, November 29, 2013.

  • M. Thomas, A stress-driven local solution approach to quasistatic brittle delamination, Seminar on Functional Analysis and Applications, International School of Advanced Studies (SISSA), Trieste, Italy, November 12, 2013.

  • M. Thomas, Mathematical modeling, analysis and optimization of strained germanium microbridges, sc Matheon Center Days, Technische Universität Berlin, November 5, 2013.

  • A. Fiebach, A. Glitzky, K. Gärtner, A. Linke, Voronoi finite volume methods for reaction-diffusion systems, MoMaS Multiphase Seminar Days --- Journées MoMaS Multiphasiques, Bures-sur-Yvette, France, October 7 - 9, 2013.

  • A. Mielke, Gradient structures and dissipation distances for reaction-diffusion systems, Workshop ``Material Theory'', December 16 - 20, 2013, Mathematisches Forschungsinstitut Oberwolfach, December 17, 2013.

  • A. Mielke, Analysis, modeling, and simulation of semiconductor devices, Kolloquium Simulation Technology, Universität Stuttgart, SRC Simulation Technology, May 14, 2013.

  • A. Mielke, Coupling quantum mechanical systems with dissipative environments via GENERIC, Applied Analysis Seminar, University of Bath, Department of Mathematical Sciences, UK, May 23, 2013.

  • A. Mielke, Thermodynamic modeling of the Maxwell--Bloch and the semiconductor equations via GENERIC, Modeling, Analysis and Simulation of Optical Modes in Photonic Devices (MASOMO 13), April 10 - 12, 2013, WIAS Berlin, April 10, 2013.

  • A. Mielke, Using gradient structures for modeling semiconductors, Eindhoven University of Technology, Institute for Complex Molecular Systems, Netherlands, February 21, 2013.

  • TH. Koprucki, K. Gärtner, A. Wilms, U. Bandelow, A. Mielke, Multidimensional modeling and simulation of quantum-dot lasers, Fachtagung Leibniz-Nano (1. Nanotechnologie-Workshop der Leibniz-Gemeinschaft), Berlin, January 30 - 31, 2012.

  • TH. Koprucki, Discretization scheme for drift-diffusion equations with strong diffusion enhancement, 12th International Conference on Numerical Simulation of Optoelectronic Devices NUSOD'12, August 28 - 31, 2012, Chinese Academy of Science, Shanghai Institute for Technical Physics, August 29, 2012.

  • M. Liero, Interfaces in solar cells, 5th Annual Meeting Photonic Devices, February 23, 2012, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, February 24, 2012.

  • M. Liero, WIAS-TeSCA simulations in photovoltaics for a point contact concept of heterojunction thin film solar cells, International Workshop ``Mathematics for Semiconductur Heterostructures: Modeling, Analysis, and Numerics'', September 24 - 28, 2012, WIAS Berlin, September 25, 2012.

  • A. Linke, Coupled flows and poor mass conservation, Workshop ``Complex grids and fluid flows, conclusion of VFSitCom, National Research Project'', April 2 - 4, 2012, Rhône-Alpes, Lyon, France, April 3, 2012.

  • A. Pérez-Serrano, J. Javaloyes, S. Balle, Multiple channel wavelength conversion using a semiconductor ring laser, European Semiconductor Laser Workshop 2012, September 20 - 23, 2012, Vrije Universiteit Brussel, Brussels, Belgium, September 21, 2012.

  • A. Glitzky, Mathematische Modellierung und Simulation organischer Halbleiterbauelemente, Senatsausschuss Wettbewerb (SAW), Sektion D der Leibniz-Gemeinschaft, Leibniz-Institut für Analytische Wissenschaften (ISAS), Dortmund, September 14, 2012.

  • M. Thomas, A model for rate-independent, brittle delamination in thermo-visco-elasticity, International Workshop on Evolution Problems in Damage, Plasticity, and Fracture: Mathematical Models and Numerical Analysis, September 19 - 21, 2012, University of Udine, Department of Mathematics, Italy, September 21, 2012.

  • M. Thomas, A model for rate-independent, brittle delamination in thermo-visco-elasticity, INDAM Workshop PDEs for Multiphase Advanced Materials (ADMAT2012), September 17 - 21, 2012, Cortona, Italy, September 17, 2012.

  • M. Thomas, Coupling of reaction-diffusion processes with thermomechanics using GENERIC, Winter School ``Calculus of Variations in Physics and Materials Science'', Würzburg, January 8 - 13, 2012.

  • M. Thomas, Thermomechanical modeling via energy and entropy, Seminar on Applied Mathematics, University of Pavia, Department of Mathematics, Italy, February 14, 2012.

  • M. Thomas, Thermomechanical modeling via energy and entropy using GENERIC, Workshop ``Mechanics of Materials'', March 19 - 23, 2012, Mathematisches Forschungsinstitut Oberwolfach, March 22, 2012.

  • K. Gärtner, A. Glitzky, Mathematics and simulation of the charge transport in semiconductor sensors, Fachtagung Leibniz-Nano (1. Nanotechnologie-Workshop der Leibniz-Gemeinschaft), Berlin, January 30 - 31, 2012.

  • A. Mielke, Multidimensional modeling and simulation of optoelectronic devices, Challenge Workshop ``Modeling, Simulation and Optimisation Tools'', September 24 - 26, 2012, Technische Universität Berlin, September 24, 2012.

  • A. Mielke, On gradient flows and reaction-diffusion systems, Institutskolloquium, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, December 3, 2012.

  • P.N. Racec, Finite volume discretization and R-matrix formalism for cylindrical nanowire heterostructures, Seminar Laboratory 30 ``Nanoscale Condensed Matter Laboratory'', National Institute of Materials Physics, Bucharest, Romania, October 9, 2012.

  • P.N. Racec, Optimal finite volume discretization of Schrödinger equations for cylindrical symmetric nanowires, 76. Jahrestagung der DPG und DPG Frühjahrstagung 2012 of the Condensed Matter Section, Sektion ``Semiconductor Physics Division'', Sitzung ``Quanum Dots and Wires: Transport Properties I'', March 26 - 29, 2012, Technische Universität Berlin, March 28, 2012.

  • A. Fiebach, K. Gärtner, Finite-volume-approximation of the Michaelis--Menten kinetics, 3rd Spring School ``Analytical and Numerical Aspects of Evolution Equations'', Essen, March 28 - April 1, 2011.

  • A. Glitzky, J.A. Griepentrog, Discrete Sobolev--Poincaré inequalities for Voronoi finite volume approximations, Finite Volumes for Complex Applications VI (FVCA 6), Prague, Czech Republic, June 6 - 10, 2011.

  • D. Knees, Numerical convergence analysis for a vanishing viscosity model in fracture mechanics, 7th International Congress on Industrial and Applied Mathematics, Session ``Materials Science II'', July 18 - 22, 2011, Society for Industrial and Applied Mathematics, Vancouver, Canada, July 19, 2011.

  • P.N. Racec, R-matrix and finite volume method for cylindrical nanowire heterostructures, Mathematical Challenges of Quantum Transport in Nano-Optoelectronic Systems, February 4 - 5, 2011, WIAS, February 4, 2011.

  • A. Caiazzo, Atlas-based reduced order modeling for fast patient-specifc simulations, 16th International Conference on Finite Elements in Flow Problems (FEF 2011), March 23 - 25, 2011, Arabellapark Hotel, München, March 24, 2011.

  • A. Caiazzo, Implicit coupling of dissipative boundary conditions models with projection schemes for Navier--Stokes equations, Workshop on Venous Hemodynamics, Medical Problems and Mathematical Modelling, October 25 - 26, 2011, Povo, Trento, Italy, October 26, 2011.

  • A.G. Vladimirov, Interaction of dissipative solitons and pulses in laser systems, Université Libre de Bruxelles, Optique Nonlinéaire Théorique, Belgium, April 21, 2010.

  • A.G. Vladimirov, Localized structures of light and their interaction, Imperial College London, Department of Applied Mathematics, UK, April 27, 2010.

  • A. Caiazzo, Blood flow through a porous interface: Numerical schemes and applications, IV International Symposium on Modeling of Physiological Flows 2010 (MPF2010), June 2 - 5, 2010, Cagliari, Italy, June 5, 2010.

  • A. Glitzky, Existence of bounded steady state solutions to spin-polarized drift-diffusion systems, Workshop on Drift Diffusion Systems and Related Problems: Analysis, Algorithms and Computations, WIAS, Research Group ``Numerical Mathematics and Scientific Computing'', March 25, 2010.

  • A. Glitzky, Uniform exponential decay of the free energy for Voronoi finite volume discretized reaction-diffusion systems, 8th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Special Session on Reaction Diffusion Systems, May 25 - 28, 2010, Technische Universität Dresden, May 26, 2010.

  • A. Mielke, The GENERIC formulation for dissipative temperature-dependent materials, International Symposium on Trends in Applications of Mathematics to Mechanics (STAMM 2010), August 30 - September 2, 2010, Technische Universität Berlin, Institut für Mechanik, Berlin, September 1, 2010.

  • H. Stephan, Evolution equations conserving positivity, Colloquium of Centre for Analysis, Scientific Computing and Applications (CASA), Technische Universiteit Einhoven, Netherlands, April 21, 2010.

  • A. Fiebach, J. Fuhrmann, Numerical issues for reaction-diffusion processes in semiconductor photoresists, Workshop ``Evolution Equations, Related Topics and Applications'', München, September 7 - 11, 2009.

  • K. Hoke, Hartree solution of the Kohn--Sham system for semiconductor devices, Berlin-Leipzig Seminar on Numerics, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, March 18, 2009.

  • K. Hoke, Iterative solution of the Kohn--Sham system for semiconductor devices, International Conference ``Mathematics of Finite Elements and Applications 2009 (MAFELAP)'', Minisymposium ``Numerical Problems in Density Functional Theory'', June 9 - 12, 2009, The Brunel Institute of Computational Mathematics (BICOM), Uxbridge, UK, June 12, 2009.

  • A. Linke, Divergence-free mixed finite elements for the incompressible Navier--Stokes equations, Universität Stuttgart, Institut für Wasserbau, December 8, 2009.

  • A. Petrov, On the error estimates for space-time discretizations of rate-independent processes, 8th GAMM Seminar on Microstructures, January 15 - 17, 2009, Universität Regensburg, NWF-I Mathematik, January 17, 2009.

  • A. Petrov, On the existence and error bounds for space-time discretizations of a 3D model for shape-memory alloys, Lisbon University, Center for Mathematics and Fundamental Applications, Portugal, September 17, 2009.

  • A. Petrov, On the numerical approximation of a viscoelastic problem with unilateral constrains, 7th EUROMECH Solid Mechanics Conference (ESMC2009), Minisymposium on Contact Mechanics, September 7 - 11, 2009, Instituto Superior Técnico, Lisbon, Portugal, September 8, 2009.

  • A.G. Vladimirov, Enhancement of interaction of dissipative solitons above self-pulsing instability threshold, CPNLW09 Soliton 2009 ``Solitons in Their Roaring Forties: Coherence and Persistence in Nonlinear Waves'', January 6 - 9, 2009, Nice University, Nice, France, January 8, 2009.

  • A.G. Vladimirov, Spontaneous motion of dissipative solitons under the effect of delay, Australasian Conference on Optics, Lasers and Spectroscopy and Australian Conference on Optical Fibre Technology in association with the International Workshop on Dissipative Solitons (ACOLS ACOFT DS 2009), November 29 - December 3, 2009, University of Adelaide, Australia, December 1, 2009.

  • A.G. Vladimirov, Strong enhancement of interaction of optical pulses induced by oscillatory instability, European Conference on Lasers and Electro-Optics and the XIth European Quantum Electronics Conference 2009 (CLEOtextsuperscript®/Europe -- EQEC 2009, Munich, June 14 - 19, 2009.

  • U. Bandelow, Solitary wave solutions for few-cycle optical pulses, WIAS Workshop ``Nonlinear Optics in Guided Geometries'', May 18 - 20, 2009, WIAS, Berlin, May 19, 2009.

  • W. Dreyer, Stochastic evolution of many particle storage systems, 9th Hirschegg Workshop on Conservation Laws, September 6 - 12, 2009, Hirschegg, September 10, 2009.

  • M. Ehrhardt, J. Fuhrmann, A. Linke, Finite volume methods for the simulation of flow cell experiments, Workshop ``New Trends in Model Coupling --- Theory, Numerics & Applications'' (NTMC'09), Paris, France, September 2 - 4, 2009.

  • M. Ehrhardt, The fluid-porous interface problem: Analytic and numerical solutions to flow cell problems, 6th Symposium on Fuel Cell Modelling and Experimental Validation (MODVAL 6), March 25 - 26, 2009, Evangelische Akademie Baden, Bad Herrenalb, March 26, 2009.

  • M. Ehrhardt, The fluid-porous interface problem: Analytic and numerical solutions to flow cell problems, Mathematical Models in Medicine, Business, Engineering (XI JORNADAS IMM), September 8 - 11, 2009, Technical University of Valencia, Institute of Multidisciplinary Mathematics, Spain, September 10, 2009.

  • J. Fuhrmann, A. Fiebach, A. Erdmann, P. Trefonas, Acid diffusion effects between resists in freezing processes used for contact hole patterning, 35th International Conference on Micro and Nano Engineering (MNE 2009), Ghent, Belgium, September 29 - 30, 2009.

  • J. Fuhrmann, Mathematical and numerical modeling of fuel cells and electrochemical flow cells, Fraunhofer-Institut für Techno- und Wirtschaftsmathematik, Kaiserslautern, December 1, 2009.

  • J. Fuhrmann, Mathematical and numerical models of electrochemical processes related to porous media, International Conference on Non-linearities and Upscaling in Porous Media (NUPUS), October 5 - 7, 2009, Universität Stuttgart, October 6, 2009.

  • J. Fuhrmann, Model based numerical impedance calculation in electrochemical systems, 6th Symposium on Fuel Cell Modelling and Experimental Validation (MODVAL 6), March 25 - 26, 2009, Evangelische Akademie Baden, Bad Herrenalb, March 25, 2009.

  • J. Fuhrmann, Modeling and simulation of post exposure bake processes in double patterning, 7th Fraunhofer IISB Lithography Simulation Workshop, September 25 - 27, 2009, Hersbruck, September 26, 2009.

  • J. Fuhrmann, Modeling of reaction diffusion problems in semiconductor photoresists, Seventh Negev Applied Mathematical Workshop, July 6 - 8, 2009, Ben Gurion University of the Negev, Jacob Blaustein Institute for Desert Research, Sede Boqer Campus, Israel, July 8, 2009.

  • J. Fuhrmann, Numerical modeling in electrochemistry, Conference on Scientific Computing (ALGORITMY 2009), March 15 - 20, 2009, Slovak University of Technology, Department of Mathematics and Descriptive Geometry, Podbanské, March 17, 2005.

  • J. Fuhrmann, Reaction-diffusion processes in polymer resists, Workshop ``Evolution Equations, Related Topics and Applications'', September 7 - 11, 2009, Helmholz-Zentrum München, September 8, 2009.

  • K. Gärtner, J.A. Griepentrog, H. Langmach, The van Roosbroeck system, its mathematical properties, and detector simulation examples, 11th European Symposium on Semiconductor Detectors, Wildbad Kreuth, June 7 - 11, 2009.

  • K. Gärtner, Charge explosion studies, 5th Meeting of the Detector Advisory Committee for the European XFEL, April 28 - 29, 2009, European XDAC, Hamburg, April 28, 2009.

  • A. Glitzky, Discrete Sobolev--Poincaré inequalities for finite volume Voronoi approximations, Annual Meeting of the Deutsche Mathematiker-Vereinigung and 17th Congress of the Österreichische Mathematische Gesellschaft, Section ``Partial Differential Equations'', September 20 - 25, 2009, Technische Universität Graz, Austria, September 21, 2009.

  • A. Glitzky, Discrete Sobolev--Poincaré inequalities using the $W^1,p$ seminorm in the setting of Voronoi finite volume approximations, International Conference on Elliptic and Parabolic Equations, November 30 - December 4, 2009, WIAS, December 3, 2009.

  • V. John, On the numerical simulation of population balance systems, Karlsruher Institut für Technologie, Fakultät für Mathematik, December 9, 2009.

  • A. Linke, Mass conservative coupling of fluid flow and species transport in electrochemical flow cells, 13th Conference on Mathematics of Finite Elements and Applications (MAFELAP 2009), June 9 - 12, 2009, Brunel University, London, UK, June 10, 2009.

  • A. Linke, The discretization of coupled flows and the problem of mass conservation, Workshop on Discretization Methods for Viscous Flows, Part II: Compressible and Incompressible Flows, June 24 - 26, 2009, Porquerolles, Toulon, France, June 25, 2009.

  • A. Linke, The discretization of coupled flows and the problem of mass conservation, Seventh Negev Applied Mathematical Workshop, July 6 - 8, 2009, Ben Gurion University of the Negev, Jacob Blaustein Institute for Desert Research, Sede Boqer Campus, Israel, July 7, 2009.

  • H. Stephan, Inequalities for Markov operators, Positivity VI (Sixth Edition of the International Conference on Positivity and its Applications), July 20 - 24, 2009, El Escorial, Madrid, Spain, July 24, 2009.

  • H. Stephan, Modeling of diffusion prozesses with hidden degrees of freedom, Workshop on Numerical Methods for Applications, November 5 - 6, 2009, Lanke, November 6, 2009.

  • A. Fiebach, J. Fuhrmann, Some reaction diffusion problems in semiconductor device fabrication, Workshop on PDE Approximations in Fast Reaction -- Slow Diffusion Scenarios, Leiden, Netherlands, November 10 - 14, 2008.

  • K. Hoke, Numerical treatment of the Kohn--Sham system for semiconductor devices, Workshop on Mathematical Aspects of Transport in Mesoscopic Systems, Dublin, Ireland, December 4 - 7, 2008.

  • K. Hoke, On the numerics of the 3D Kohn--Sham system, 4th Workshop on Mathematical Models for Transport in Macroscopic and Mesoscopic Systems, February 8 - 9, 2008, WIAS, February 9, 2008.

  • E. Holzbecher, H. Zhao, J. Fuhrmann, A. Linke, H. Langmach, Numerical investigation of thin layer flow cells, 4th Gerischer Symposium, Berlin, June 25 - 27, 2008.

  • A. Petrov, Error estimates for space-time discretizations of a 3D model for shape-memory materials, IUTAM Symposium ``Variational Concepts with Applications to the Mechanics of Materials'', September 22 - 26, 2008, Ruhr-Universität Bochum, Lehrstuhl für allgemeine Mechanik, September 24, 2008.

  • A. Petrov, Existence and approximation for 3D model of thermally induced phase transformation in shape-memory alloys, 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2008), Session ``Material models in solids'', March 31 - April 4, 2008, Universität Bremen, April 1, 2008.

  • A. Petrov, Some mathematical results for a model of thermally-induced phase transformations in shape-memory materials, sc Matheon--ICM Workshop on Free Boundaries and Materials Modeling, March 17 - 18, 2008, WIAS, March 18, 2008.

  • A.G. Vladimirov, Nonlinear dynamics of pulse interactions in bistable optical systems, V International Conference ``Basic Problems of Optics'' BPO-2008 in the framework of V International Congress ``Optics - XXI century'', October 20 - 24, 2008, St Petersburg, Russian Federation, October 23, 2008.

  • E. Bänsch, H. Berninger, U. Böhm, A. Bronstert, M. Ehrhardt, R. Forster, J. Fuhrmann, R. Klein, R. Kornhuber, A. Linke, A. Owinoh, J. Volkholz, Pakt für Forschung und Innovation: Das Forschungsnetzwerk ``Gekoppelte Strömungsprozesse in Energie- und Umweltforschung'', Show of the Leibniz Association ``Exzellenz durch Vernetzung. Kooperationsprojekte der deutschen Wissenschaftsorganisationen mit Hochschulen im Pakt für Forschung und Innovation'', Berlin, November 12, 2008.

  • U. Bandelow, Solitary wave solutions for ultrashort optical pulses, Technical Conference ``Frontiers in Optics 2008, Laser Science XXIV'', October 19 - 23, 2008, Optical Society of America (OSA), Rochester, USA, October 21, 2008.

  • M. Ehrhardt, O. Gloger, Th. Dietrich, O. Hellwich, K. Graf, E. Nagel, Level Set Methoden zur Segmentierung von kardiologischen MR-Bildern, 22. Treffpunkt Medizintechnik: Fortschritte in der medizinischen Bildgebung, Charité, Campus Virchow Klinikum Berlin, May 22, 2008.

  • I. Kanattšikow, The short pulse equation: Integrability and generalizations, Gdańsk University of Technology, Institute of Theoretical Physics and Quantum Informatics, Gdańsk, Poland, June 30, 2008.

  • A. Linke, Mass conservative coupling of fluid flow and species transport in electrochemical flow cells, Annual Meeting of the Deutsche Mathematiker-Vereinigung 2008, September 15 - 19, 2008, Friedrich-Alexander-Universität Erlangen-Nürnberg, September 16, 2008.

  • A. Linke, Mass conservative coupling of fluid flow and species transport in electrochemical flow cells, Georg-August-Universität Göttingen, November 11, 2008.

  • A. Linke, Lowest-order Scott--Vogelius elements for the incompressible Navier--Stokes equation, Universität Göttingen, Institut für Numerische und Angewandte Mathematik, January 10, 2007.

  • A. Linke, Non-nested multi-grid solvers for mixed divergence-free Scott-Vogelius discretizations, 20th Chemnitz FEM Symposium, September 24 - 26, 2007, Technische Universität Chemnitz, Fakultät für Mathematik, September 26, 2007.

  • A. Linke, Stabilized finite element schemes for incompressible flow using Scott-Vogelius elements, Université de Marne-la-Vallée, Département de Mathématiques, Champs-sur-Marne, France, April 19, 2007.

  • A. Linke, Stabilized finite element schemes for incompressible flow using Scott-Vogelius elements, Friedrich-Alexander-Universität Erlangen-Nürnberg, Angewandte Mathematik III, July 3, 2007.

  • M. Pietrzyk, Multisymplectic analysis of the short pulse equation, 10th International Conference on Differential Geometry and Its Application, August 27 - 31, 2007, Olomouc, Czech Republic, August 28, 2007.

  • M. Lichtner, Invariant manifold theorem for semilinear hyperbolic systems, EQUADIFF 07, August 5 - 11, 2007, Technische Universität Wien, Austria, August 7, 2007.

  • A. Vladimirov, Autosolitons in optical devices with transverse refractive index modulation, International Conference on Coherent and Nonlinear Optics/International Conference on Lasers, Applications, and Technologies (ICONO/LAT 2007), May 28 - June 1, 2007, Minsk, Belarus, May 29, 2007.

  • A. Vladimirov, Dissipative solitons in nonlinear optical devices with refractive index modulation, Workshop ``Nonlinear Effects in Photonic Materials'', March 12 - 14, 2007, WIAS, Berlin, March 14, 2007.

  • M. Lichtner, A spectral gap mapping theorem and smooth invariant center manifolds for semilinear hyperbolic systems, 6th AIMS International Conference on Dynamical Systems, Differential Equations & Applications, June 25 - 28, 2006, Université de Poitiers, France, June 28, 2006.

  • A. Linke, Computing generalized Oseen flows by stabilized lowest-order Scott-Vogelius elements, Friedrich-Alexander-Universität Erlangen-Nürnberg, Angewandte Mathematik III, July 21, 2006.

  • A. Vladimirov, Laser dissipative solitons and their interaction, Minisymposium on Dissipative Solitons, WIAS, Berlin, April 20, 2006.

  • A. Vladimirov, Localized structures of light in laser systems and their weak interactions, Technische Universität Berlin, June 14, 2006.

  • A. Vladimirov, Nonlinear dynamics and bifurcations in multimode and spatially distributed laser systems, June 20 - 23, 2006, St. Petersburg State University, Russian Federation, June 20, 2006.

  • A. Vladimirov, Nonlinear dynamics in multimode and spatially extended laser systems, Moscow State University, Physics Faculty, Russian Federation, November 10, 2006.

  • A. Vladimirov, Transverse Bragg dissipative solitons in a Kerr cavity with refractive index modulation, Laser Optics Conference, June 26 - 30, 2006, St. Petersburg, Russian Federation, June 28, 2006.

  • A. Vladimirov, G. Kozyreff, P. Mandel, M. Tlidi, Localized structures in a passive cavity with refractive index modulation, International Quantum Electronics Conference, June 12 - 17, 2005, München, June 15, 2005.

  • A. Vladimirov, Interaction of dissipative solitons in laser systems, Ben Gurion University of the Negev, Department of Mathematics, Beer Sheva, Israel, November 17, 2005.

  • D. Turaev, S. Zelik, A. Vladimirov, Chaotic bound state of localized structures in the complex Ginzburg--Landau equation, Conference Digest ``Nonlinear Guided Waves and their Applications'', Dresden, September 6 - 9, 2005.

  • J. Fuhrmann, H.-Chr. Kaiser, Th. Koprucki, G. Schmidt, Electronic states in semiconductor nanostructures and upscaling to semi-classical models, Evaluation Colloquium of the DFG Priority Program ``Analysis, Modeling and Simulation of Multiscale Problems'', Bad Honnef, May 20 - 21, 2004.

  • H.-Chr. Kaiser, On space discretization of reaction-diffusion systems with discontinuous coefficients and mixed boundary conditions, 2nd GAMM Seminar on Microstructures, January 10 - 11, 2003, Ruhr-Universität Bochum, Institut für Mechanik, January 10, 2003.

  • A. Vladimirov, Moving discrete solitons in multicore fibers and waveguide arrays, European Quantum Electronics Conference, June 22 - 27, 2003, München, June 25, 2003.

  • A. Vladimirov, Moving discrete solitons in multicore fibers and waveguide arrays, Conference dedicated to the 60th birthday of Prof. Paul Mandel, April 11 - 12, 2003, Université Libre de Bruxelles, Optique Nonlinéaire Théorique, Belgium, April 11, 2003.

  External Preprints

  • G.R. Barrenechea, V. John, P. Knobloch, An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes, Preprint no. 2016-06, Nečas Center for Mathematical Modeling, 2016.

  • S. Neukamm, A. Gloria, F. Otto, An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations, Preprint no. 41, Max-Planck-Institut für Mathematik in den Naturwissenschaften, 2013.
    Abstract
    We establish an optimal, linear rate of convergence for the stochastic homogenization of discrete linear elliptic equations. We consider the model problem of independent and identically distributed coefficients on a discretized unit torus. We show that the difference between the solution to the random problem on the discretized torus and the first two terms of the two-scale asymptotic expansion has the same scaling as in the periodic case. In particular the L2-norm in probability of the H1-norm in space of this error scales like ε, where ε is the discretization parameter of the unit torus. The proof makes extensive use of previous results by the authors, and of recent annealed estimates on the Greens function by Marahrens and the third author.

  • S. Amiranashvili, U. Bandelow, A.G. Vladimirov, Solitary wave solutions for few-cycle optical pulses, Preprint no. 500, DFG Research Center sc Matheon, 2008.