Publikationen
Monografien

R. Ahrens, Z. Lakdawala, A. Voigt, V. Wiedmeyer, V. John, S. Le Borne, K. Sundmacher, Numerical Methods for Coupled Population Balance Systems Applied to the Dynamical Simulation of Crystallization Processes, S. Heinrich, ed., Dynamic Flowsheet Simulation of Solids Processes, Springer, Cham, 2020, pp. 475518, (Chapter Published), DOI 10.1007/9783030451684_14 .

V. John, P. Knobloch, U. Wilbrandt, Finite Element Pressure Stabilizations for Incompressible Flow Problems, T. Bodnár, G. Galdi, Š. Nečasová, eds., Fluids Under Pressure, Birkhäuser, Cham, 2020, pp. pp 483573, (Chapter Published), DOI 10.1007/9783030396398_6 .
Abstract
Discretizations of incompressible flow problems with pairs of finite element spaces that do not satisfy a discrete infsup condition require a socalled pressure stabilization. This paper gives an overview and systematic assessment of stabilized methods, including the respective error analysis. 
R. Klöfkorn, E. Keilegavlen, F.A. Radu , J. Fuhrmann, eds., Finite Volumes for Complex Applications IX  Methods, Theoretical Aspects, Examples  FVCA 9, Bergen, June 2020, 323 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2014, 775 pages, (Collection Published), DOI 10.1007/9783030436513 .
Artikel in Referierten Journalen

TH. Apel, V. Kempf, A. Linke, Ch. Merdon, A nonconforming pressurerobust finite element method for the Stokes equations on anisotropic meshes, IMA Journal of Numerical Analysis, published online on 14.01.2021, DOI 10.1093/imanum/draa097 .
Abstract
Most classical finite element schemes for the (Navier)Stokes equations are neither pressurerobust, nor are they infsup stable on general anisotropic triangulations. A lack of pressurerobustness may lead to large velocity errors, whenever the Stokes momentum balance is dominated by a strong and complicated pressure gradient. It is a consequence of a method, which does not exactly satisfy the divergence constraint. However, infsup stable schemes can often be made pressurerobust just by a recent, modified discretization of the exterior forcing term, using H(div)conforming velocity reconstruction operators. This approach has so far only been analyzed on shaperegular triangulations. The novelty of the present contribution is that the reconstruction approach for the CrouzeixRaviart method, which has a stable Fortin operator on arbitrary meshes, is combined with results on the interpolation error on anisotropic elements for reconstruction operators of RaviartThomas and BrezziDouglasMarini type, generalizing the method to a large class of anisotropic triangulations. Numerical examples confirm the theoretical results in a 2D and a 3D test case. 
A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, Th. Koprucki, Numerical simulation of TEM images for In(Ga)As/GaAs quantum dots with various shapes, Optical and Quantum Electronics, 52 (2020), pp. 257/1257/11 (published online on 05.05.2020), DOI 10.1007/s1108202002356y .
Abstract
We present a mathematical model and a tool chain for the numerical simulation of TEM images of semiconductor quantum dots (QDs). This includes elasticity theory to obtain the strain profile coupled with the DarwinHowieWhelan equations, describing the propagation of the electron wave through the sample. We perform a simulation study on indium gallium arsenide QDs with different shapes and compare the resulting TEM images to experimental ones. This tool chain can be applied to generate a database of simulated TEM images, which is a key element of a novel concept for modelbased geometry reconstruction of semiconductor QDs, involving machine learning techniques. 
W. Dreyer, P.É. Druet, P. Gajewski, C. Guhlke, Analysis of improved NernstPlanckPoisson models of compressible isothermal electrolytes, ZAMP Zeitschrift fur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Mathematiques et de Physique Appliquees, 71 (2020), pp. 119/1119/68, DOI 10.1007/s00033020013415 .
Abstract
We consider an improved NernstPlanckPoisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non equilibrium. The model takes into account the elastic deformation of the medium that induces an inherent coupling of mass and momentum transport. The model consists of convectiondiffusionreaction equations for the constituents of the mixture, of the NavierStokes equation for the barycentric velocity, and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, crossdiffusion phenomena must occur and the mobility matrix (Onsager matrix) has a kernel. In this paper we establish the existence of a globalintime weak solution for the full model, allowing for a general structure of the mobility tensor and for chemical reactions with highly non linear rates in the bulk and on the active boundary. We characterise the singular states of the system, showing that the chemical species can vanish only globally in space, and that this phenomenon must be concentrated in a compact set of measure zero in time. With respect to our former study [DDGG16], we also essentially improve the a priori estimates, in particular concerning the relative chemical potentials. 
P. Vágner, M. Pavelka, O. Esen, Multiscale thermodynamics of charged mixtures, Continuum Mechanics and Thermodynamics, (2020), published online on 25.07.2020, DOI 10.1007/s00161020009005 .
Abstract
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely geometric way by means of semidirect products. This leads to a complex Hamiltonian system with a new Poisson bracket, which can be used in principle with any energy functional. The thermodynamic (irreversible) part is added as gradient dynamics, generated by derivatives of a dissipation potential, which makes the theory part of the GENERIC framework. Subsequently, Dynamic MaxEnt reductions are carried out, which lead to reduced GENERIC models for smaller sets of state variables. Eventually, standard engineering models are recovered as the lowlevel limits of the detailed theory. The theory is then compared to recent literature. 
M. Akbas, Th. Gallouët, A. Gassmann, A. Linke, Ch. Merdon, A gradientrobust wellbalanced scheme for the compressible isothermal Stokes problem, Computer Methods in Applied Mechanics and Engineering, 367 (2020), 113069, DOI 10.1016/j.cma.2020.113069 .
Abstract
A novel notion for constructing a wellbalanced scheme  a gradientrobust scheme  is introduced and a showcase application for a steady compressible, isothermal Stokes equations is presented. Gradientrobustness means that arbitrary gradient fields in the momentum balance are wellbalanced by the discrete pressure gradient  if there is enough mass in the system to compensate the force. The scheme is asymptoticpreserving in the sense that it degenerates for low Mach numbers to a recent infsup stable and pressurerobust discretization for the incompressible Stokes equations. The convergence of the coupled FEMFVM scheme for the nonlinear, isothermal Stokes equations is proved by compactness arguments. Numerical examples illustrate the numerical analysis, and show that the novel approach can lead to a dramatically increased accuracy in nearlyhydrostatic low Mach number flows. Numerical examples also suggest that a straightforward extension to barotropic situations with nonlinear equations of state is feasible. 
N. Ahmed, V. John, An assessment of two classes of variational multiscale methods for the simulation of incompressible turbulent flows, Computer Methods in Applied Mechanics and Engineering, 365 (2020), pp. 112997/1112997/20, DOI 10.1016/j.cma.2020.112997 .
Abstract
A numerical assessment of two classes of variational multiscale (VMS) methods for the simulation of incompressible flows is presented. Two types of residualbased VMS methods and two types of projectionbased VMS methods are included in this assessment. The numerical simulations are performed at turbulent channel flow problems with various friction Reynolds numbers. It turns out the the residualbased VMS methods, in particular when used with a pair of infsup stable finite elements, give usually the most accurate results for second order statistics. For this pair of finite element spaces, a flexible GMRES method with a Least Squares Commutator (LSC) preconditioner proved to be an efficient solver. 
C. Cancès, C. ChainaisHillairet, J. Fuhrmann, B. Gaudeul, A numerical analysis focused comparison of several finite volume schemes for an unipolar degenerated driftdiffusion model, IMA Journal of Numerical Analysis, published on 17.07.2020, DOI 10.1093/imanum/draa002 .
Abstract
In this paper, we consider an unipolar degenerated driftdiffusion system where the relation between the concentration of the charged species c and the chemical potential h is h(c) = log ^{c}/_{1c}. We design four different finite volume schemes based on four different formulations of the fluxes. We provide a stability analysis and existence results for the four schemes. The convergence proof with respect to the discretization parameters is established for two of them. Numerical experiments illustrate the behaviour of the different schemes. 
D.H. Doan, A. Fischer, J. Fuhrmann, A. Glitzky, M. Liero, Driftdiffusion simulation of Sshaped currentvoltage relations for organic semiconductor devices, Journal of Computational Electronics, 19 (2020), pp. 11641174, DOI 10.1007/s10825020015056 .
Abstract
We present an electrothermal driftdiffusion model for organic semiconductor devices with GaussFermi statistics and positive temperature feedback for the charge carrier mobilities. We apply temperature dependent Ohmic contact boundary conditions for the electrostatic potential and discretize the system by a finite volume based generalized ScharfetterGummel scheme. Using pathfollowing techniques we demonstrate that the model exhibits Sshaped currentvoltage curves with regions of negative differential resistance, which were only recently observed experimentally. 
B. GarcíaArchilla, V. John, J. Novo, Symmetric pressure stabilization for equalorder finite element approximations to the timedependent NavierStokes equations, IMA Journal of Numerical Analysis, (2020), pp. draa037/1draa037/34, DOI 10.1093/imanum/draa037 .

D. Janke, A. Caiazzo, N. Ahmed, N. Alia, O. Knoth, B. Moreau, U. Wilbrandt, D. Willink, Th. Amon, V. John, On the feasibility of using open source solvers for the simulation of a turbulent air flow in a dairy barn, Computers and Electronics in Agriculture, 175 (2020), pp. 105546/1105546/16, DOI 10.1016/j.compag.2020.105546 .
Abstract
Two transient open source solvers, OpenFOAM and ParMooN, are assessed with respect to the simulation of the turbulent air flow inside and around a dairy barn. For this purpose, data were obtained in an experimental campaign at a 1:100 scaled wind tunnel model. Both solvers used different meshes, discretization schemes, and turbulence models. The experimental data and numerical results agree well for timeaveraged streamwise and verticalwise velocities. In particular, the air exchange was predicted with high accuracy by both solvers with relative errors less than 5 % compared to the experimental results. With respect to the turbulent quantities, good agreements at the second (downwind) half of the barn inside and especially outside the barn could be achieved, where both codes accurately predicted the flow separation and the rootmeansquare velocities. Deviations between simulations and experimental results regarding turbulent quantities could be observed in the first part of the barn, due to different inlet conditions between the experimental setup and the numerical simulations. Both solvers proved to be promising tools for the accurate prediction of timedependent phenomena in an agricultural context, e.g., like the transport of particulate matter or pathogenladen aerosols in and around agricultural buildings. 
A. Kirch, A. Fischer, M. Liero, J. Fuhrmann, A. Glitzky, S. Reineke, Experimental proof of Joule heatinginduced switchedback regions in OLEDs, Light: Science and Applications, 9 (2020), pp. 5/15/10, DOI 10.1038/s4137701902369 .

C.K. Macnamara, A. Caiazzo, I. RamisConde, M.A.J. Chaplain, Computational modelling and simulation of cancer growth and migration within a 3D heterogeneous tissue: The effects of fibre and vascular structure, Journal of Computational Science, 40 (2020), pp. 101067/1101067/24, DOI 10.1016/j.jocs.2019.101067 .
Abstract
The term cancer covers a multitude of bodily diseases, broadly categorised by having cells which do not behave normally. Since cancer cells can arise from any type of cell in the body, cancers can grow in or around any tissue or organ making the disease highly complex. Our research is focused on understanding the specific mechanisms that occur in the tumour microenvironment via mathematical and computational modeling. We present a 3D individualbased model which allows one to simulate the behaviour of, and spatiotemporal interactions between, cells, extracellular matrix fibres and blood vessels. Each agent (a single cell, for example) is fully realised within the model and interactions are primarily governed by mechanical forces between elements. However, as well as the mechanical interactions we also consider chemical interactions, for example, by coupling the code to a finite element solver to model the diffusion of oxygen from blood vessels to cells. The current state of the art of the model allows us to simulate tumour growth around an arbitrary bloodvessel network or along the striations of fibrous tissue. 
L.G. Ramos, R. Kehl, R. Nabben, Projections, deflation and multigrid for nonsymmetric matrices, SIAM Journal on Matrix Analysis and Applications, 41 (2020), pp. 83105, DOI 10.1016/j.jocs.2019.101067 .

J. Tang, P. Cui, B. Li, Z. Yaobin, H. Si, Parallel hybrid mesh adaptation by refinement and coarsening, Graphical Models, 111 (2020), 101084, DOI 10.1016/j.gmod.2020.101084 .

J.P. Köster, A. Putz, H. Wenzel, H.J. Wünsche, M. Radziunas, H. Stephan, M. Wilkens, A. Zeghuzi, A. Knigge, Mode competition in broadridgewaveguide lasers, Semiconductor Science and Technology, 36 (2020), pp. 015014/1015014/12, DOI 10.1088/13616641/abc6e7 .
Abstract
The lateral brightness achievable with highpower GaAsbased laser diodes having long and broad waveguides is commonly regarded to be limited by the onset of higherorder lateral modes. For the study of the lateralmode competition two complementary simulation tools are applied, representing different classes of approximations. The first tool bases on a completely incoherent superposition of mode intensities and disregards longitudinal effects like spatial hole burning, whereas the second tool relies on a simplified carrier transport and current flow. Both tools yield agreeing powercurrent characteristics that fit the data measured for 5 to 23 µm wide ridges. Also, a similarly good qualitative conformance of the near and far fields is found. However, the threshold of individual modes, the partition of power between them at a given current, and details of the near and far fields show differences. These differences are the consequence of a high sensitivity of the mode competition to details of the models and of the device structure. Nevertheless, it can be concluded concordantly that the brightness rises with increasing ridge width irrespective of the onset of more and more lateral modes. The lateral brightness 2W · mm¯¹ 1mrad¯¹ at 10MW · cm¯²2 power density on the front facet of the investigated laser with widest ridge (23 µm) is comparable with best values known from much wider broadarea lasers. In addition, we show that one of the simulation tools is able to predict beam steering and coherent beam 
L. Blank, E. Meneses Rioseco, U. Wilbrandt, A. Caiazzo, Modeling, simulation, and optimization of geothermal energy production from hot sedimentary aquifers, Computer & Geosciences, 25 (2021), pp. 67104 (published online on 02.09.2020), DOI 10.1007/s10596020099898 .
Abstract
Geothermal district heating development has been gaining momentum in Europe with numerous deep geothermal installations and projects currently under development. With the increasing density of geothermal wells, questions related to the optimal and sustainable reservoir exploitation become more and more important. A quantitative understanding of the complex thermohydraulic interaction between tightly deployed geothermal wells in heterogeneous temperature and permeability fields is key for a maximum sustainable use of geothermal resources. Motivated by the geological settings of the Upper Jurassic aquifer in the Greater Munich region, we develop a computational model based on finite element analysis and gradientfree optimization to simulate groundwater flow and heat transport in hot sedimentary aquifers, and investigate numerically the optimal positioning and spacing of multiwell systems. Based on our numerical simulations, net energy production from deep geothermal reservoirs in sedimentary basins by smart geothermal multiwell arrangements provides significant amounts of energy to meet heat demand in highly urbanized regions. Our results show that taking into account heterogeneous permeability structures and variable reservoir temperature may drastically affect the results in the optimal configuration. We demonstrate that the proposed numerical framework is able to efficiently handle generic geometrical and geologocal configurations, and can be thus flexibly used in the context of multivariable optimization problems. Hence, this numerical framework can be used to assess the extractable geothermal energy from heterogeneous deep geothermal reservoirs by the optimized deployment of smart multiwell systems. 
A. Caiazzo, R. Maier, D. Peterseim, Reconstruction of quasilocal numerical effective models from lowresolution measurements, Journal of Scientific Computing, 85 (2020), pp. 10/110/23, DOI 10.1007/s1091502001304y .
Abstract
We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on lowresolution measurements. We rely on recent quasilocal numerical effective models that, in contrast to conventional homogenized models, are provably reliable beyond periodicity assumptions and scale separation. The goal of this work is to show that the identification of the matrix representation of these effective models is possible. Algorithmic aspects of the inversion procedure and its performance are illustrated in a series of numerical experiments. 
D. Frerichs, Ch. Merdon, Divergencepreserving reconstructions on polygons and a really pressurerobust virtual element method for the Stokes problem, IMA Journal of Numerical Analysis, (2020), published on 9.11.2020, DOI 10.1093/imanum/draa073 .
Abstract
Non divergencefree discretisations for the incompressible Stokes problem may suffer from a lack of pressurerobustness characterised by large discretisations errors due to irrotational forces in the momentum balance. This paper argues that also divergencefree virtual element methods (VEM) on polygonal meshes are not really pressurerobust as long as the righthand side is not discretised in a careful manner. To be able to evaluate the righthand side for the testfunctions, some explicit interpolation of the virtual testfunctions is needed that can be evaluated pointwise everywhere. The standard discretisation via an L^{2} bestapproximation does not preserve the divergence and so destroys the orthogonality between divergencefree testfunctions and possibly eminent gradient forces in the righthand side. To repair this orthogonality and restore pressurerobustness another divergencepreserving reconstruction is suggested based on RaviartThomas approximations on local subtriangulations of the polygons. All findings are proven theoretically and are demonstrated numerically in two dimensions. The construction is also interesting for hybrid highorder methods on polygonal or polyhedral meshes. 
J. Fuhrmann, M. Landstorfer, R. Müller, Modeling polycrystalline electrodeelectrolyte interfaces: The differential capacitance, Journal of The Electrochemical Society, 167 (2020), pp. 106512/1106512/15, DOI 10.1149/19457111/ab9cca .
Abstract
We present and analyze a model for polycrystalline electrode surfaces based on an improved continuum model that takes finite ion size and solvation into account. The numerical simulation of finite size facet patterns allows to study two limiting cases: While for facet size diameter $d^facet to 0$ we get the typical capacitance of a spatially homogeneous but possible amorphous or liquid surface, in the limit $L^Debye << d^facet$ , an ensemble of noninteracting single crystal surfaces is approached. Already for moderate size of the facet diameters, the capacitance is remarkably well approximated by the classical approach of adding the single crystal capacities of the contributing facets weighted by their respective surface fraction. As a consequence, the potential of zero charge is not necessarily attained at a local minimum of capacitance, but might be located at a local capacitance maximum instead. Moreover, the results show that surface roughness can be accurately taken into account by multiplication of the ideally flat polycrystalline surface capacitance with a single factor. In particular, we find that the influence of the actual geometry of the facet pattern in negligible and our theory opens the way to a stochastic description of complex real polycrystal surfaces. 
V. John, P. Knobloch, P. Korsmeier, On the solvability of the nonlinear problems in an algebraically stabilized finite element method for evolutionary transportdominated equations, Mathematics of Computation, 90 (2021), pp. 595611 (published online on 16.11.2020), DOI 10.1090/mcom/3576 .

V. John, P. Knobloch, Existence of solutions of a finite element fluxcorrectedtransport scheme, Applied Mathematics Letters, 115 (2021), pp. 106932/1106932/6 (published online on 01.12.2020), DOI 10.1016/j.aml.2020.106932 .
Abstract
The existence of a solution is proved for a nonlinear finite element fluxcorrectedtransport (FEMFCT) scheme with arbitrary time steps for evolutionary convectiondiffusionreaction equations and transport equations. 
A. Linke, Ch. Merdon, M. Neilan, Pressurerobustness in quasioptimal a priori estimates for the Stokes problem, Electronic Transactions on Numerical Analysis, 52 (2020), pp. 281294, DOI 10.1553/etna_vol52s281 .
Beiträge zu Sammelwerken

A. Linke, Ch. Merdon, On the significance of pressurerobustness for the space discretization of incompressible high reynolds number flows, in: Proceedings of Finite Volumes for Complex Applications IX  Methods, Theoretical Aspects, Examples  FVCA 9, Bergen, Norway, June 2020, R. Klöfkorn, E. Keilegavlen, A.F. Radu, J. Fuhrmann, eds., Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2020, pp. 103112.

A. Linke, Ch. Merdon, Wellbalanced discretisation for the compressible Stokes problem by gradientrobustness, in: Proceedings of Finite Volumes for Complex Applications IX  Methods, Theoretical Aspects, Examples  FVCA 9, Bergen, Norway, June 2020, R. Klöfkorn, E. Keilegavlen, A.F. Radu, J. Fuhrmann, eds., Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2020, pp. 113121.

C. Cancès, C. ChainaisHillairet, J. Fuhrmann, B. Gaudeul, On four numerical schemes for a unipolar degenerate driftdiffusion model, in: Proceedings of Finite Volumes for Complex Applications IX, Bergen, Norway, June 2020, R. Klöfkorn, F. Radu, E. Keijgavlen, J. Fuhrmann, eds., Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2020, pp. 163171, DOI 10.1007/9783030436513_13 .

A. Jha, V. John, On basic iteration schemes for nonlinear AFC discretizations, in: Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2018, G.N. Barrenechea, J. Mackenzie, eds., 135 of Lecture Notes in Computational Science and Engineering, Springer, Cham, 2020, pp. 113128, DOI https://doi.org/10.1007/9783030418007_7 .
Abstract
Algebraic flux correction (AFC) finite element discretizations of steadystate convectiondiffusionreaction equations lead to a nonlinear problem. This paper presents first steps of a systematic study of solvers for these problems. Two basic fixed point iterations and a formal Newton method are considered. It turns out that the fixed point iterations behave often quite differently. Using a sparse direct solver for the linear problems, one of them exploits the fact that only one matrix factorization is needed to become very efficient in the case of convergence. For the behavior of the formal Newton method, a clear picture is not yet obtained. 
S. Schulz, D. Chaudhuri, M. O'Donovan, S. Patra, T. Streckenbach, P. Farrell, O. Marquardt, Th. Koprucki, Multiscale modeling of electronic, optical, and transport properties of IIIN alloys and heterostructures, in: Proceedings Physics and Simulation of Optoelectronic Devices XXVIII, 11274, San Francisco, California, USA, 2020, pp. 416426, DOI 10.1117/12.2551055 .

J. Fuhrmann, D.H. Doan, A. Glitzky, M. Liero, G. Nika, Unipolar driftdiffusion simulation of Sshaped currentvoltage relations for organic semiconductor devices, in: Proceedings of ``Finite Volumes for Complex Applications IX'', R. Klöfkorn, E. Keilegavlen, F.A. Radu, J. Fuhrmann, eds., 323 of Springer Proceedings in Mathematics & Statistics, Springer, Cham, 2020, pp. 625633, DOI 10.1007/9783030436513_59 .
Abstract
We discretize a unipolar electrothermal driftdiffusion model for organic semiconductor devices with GaussFermi statistics and charge carrier mobilities having positive temperature feedback. We apply temperature dependent Ohmic contact boundary conditions for the electrostatic potential and use a finite volume based generalized ScharfetterGummel scheme. Applying pathfollowing techniques we demonstrate that the model exhibits Sshaped currentvoltage curves with regions of negative differential resistance, only recently observed experimentally.
Preprints, Reports, Technical Reports

V. Miloš, P. Vágner, D. Budáč, M. Carda, M. Paidar, J. Fuhrmann, K. Bouzek, Generalized PoissonNernstPlanckbased physical model of O_{2} LSM YSZ electrode, Preprint no. 2797, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2797 .
Abstract, PDF (781 kByte)
The paper presents a generalized PoissonNernstPlanck model of an yttriastabilized zirconia electrolyte developed from first principles of nonequilibrium thermodynamics which allows for spatial resolution of the space charge layer. It takes into account limitations in oxide ion concentrations due to the limited availability of oxygen vacancies. The electrolyte model is coupled with a reaction kinetic model describing the triple phase boundary with electron conducting lanthanum strontium manganite and gaseous phase oxygen. By comparing the outcome of numerical simulations based on different formulations of the kinetic equations with results of EIS and CV measurements we attempt to discern the existence of separate surface lattice sites for oxygen adatoms and O^{2} from the assumption of shared ones. Furthermore, we discern massaction kinetics models from exponential kinetics models. 
D. Abdel, P. Farrell, J. Fuhrmann, Assessing the quality of the excess chemical potential flux scheme for degenerate semiconductor device simulation, Preprint no. 2787, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2787 .
Abstract, PDF (682 kByte)
The van Roosbroeck system models current flows in (non)degenerate semiconductor devices. Focusing on the stationary model, we compare the excess chemical potential discretization scheme, a flux approximation which is based on a modification of the drift term in the current densities, with another stateoftheart ScharfetterGummel scheme, namely the diffusionenhanced scheme. Physically, the diffusionenhanced scheme can be interpreted as a flux approximation which modifies the thermal voltage. As a reference solution we consider an implicitly defined integral flux, using Blakemore statistics. The integral flux refers to the exact solution of a local two point boundary value problem for the continuous current density and can be interpreted as a generalized ScharfetterGummel scheme. All numerical discretization schemes can be used within a Voronoi finite volume method to simulate charge transport in (non)degenerate semiconductor devices. The investigation includes the analysis of Taylor expansions, a derivation of error estimates and a visualization of errors in local flux approximations to extend previous discussions. Additionally, driftdiffusion simulations of a pin device are performed. 
D. Abdel, P. Vágner, J. Fuhrmann, P. Farrell, Modelling charge transport in perovskite solar cells: Potentialbased and limiting ion vacancy depletion, Preprint no. 2780, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2780 .
Abstract, PDF (1067 kByte)
From MaxwellStefan diffusion and general electrostatics, we derive a driftdiffusion model for charge transport in perovskite solar cells (PSCs) where any ion in the perovskite layer may flexibly be chosen to be mobile or immobile. Unlike other models in the literature, our model is based on quasi Fermi potentials instead of densities. This allows to easily include nonlinear diffusion (based on for example FermiDirac, GaussFermi or Blakemore statistics) as well as limit the ion vacancy depletion (via the FermiDirac integral of order 1). The latter will be motivated by a grandcanonical formalism of ideal lattice gas. Furthermore, our model allows to use different statistics for different species. We discuss the thermodynamic equilibrium, electroneutrality as well as generation/recombination. Finally, we present numerical finite volume simulations to underline the importance of limiting ion vacancy depletion. 
U. Wilbrandt, N. Alia, V. John, Optimal control of a buoyancydriven liquid steel stirring modeled with singlephase NavierStokes equations, Preprint no. 2776, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2776 .
Abstract, PDF (1469 kByte)
Gas stirring is an important process used in secondary metallurgy. It allows to homogenize the temperature and the chemical composition of the liquid steel and to remove inclusions which can be detrimental for the endproduct quality. In this process, argon gas is injected from two nozzles at the bottom of the vessel and rises by buoyancy through the liquid steel thereby causing stirring, i.e., a mixing of the bath. The gas flow rates and the positions of the nozzles are two important control parameters in practice. A continuous optimization approach is pursued to find optimal values for these control variables. The effect of the gas appears as a volume force in the singlephase incompressible NavierStokes equations. Turbulence is modeled with the Smagorinsky Large Eddy Simulation (LES) model. An objective functional based on the vorticity is used to describe the mixing in the liquid bath. Optimized configurations are compared with a default one whose design is based on a setup from industrial practice. 
D. Frerichs, V. John, On reducing spurious oscillations in discontinuous Galerkin (DG) methods for steadystate convectiondiffusionreaction equations, Preprint no. 2769, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2769 .
PDF (1663 kByte) 
P.L. Lederer, Ch. Merdon, Guaranteed upper bounds for the velocity error of pressurerobust Stokes discretisations, Preprint no. 2750, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2750 .
Abstract, PDF (422 kByte)
This paper improves guaranteed error control for the Stokes problem with a focus on pressurerobustness, i.e. for discretisations that compute a discrete velocity that is independent of the exact pressure. A PragerSynge type result relates the errors of divergencefree primal and H(div)conforming dual mixed methods (for the velocity gradient) with an equilibration constraint that needs special care when discretised. To relax the constraints on the primal and dual method, a more general result is derived that enables the use of a recently developed mass conserving mixed stress discretisation to design equilibrated fluxes that yield pressureindependent guaranteed upper bounds for any pressurerobust (but not necessarily divergencefree) primal discretisation. Moreover, a provably efficient local design of the equilibrated fluxes is presented that reduces the numerical costs of the error estimator. All theoretical findings are verified by numerical examples which also show that the efficiency indices of our novel guaranteed upper bounds for the velocity error are close to 1. 
N. Ahmed, G.R. Barrenechea, E. Burman, J. Guzmán, A. Linke, Ch. Merdon, A pressurerobust discretization of Oseen's equation using stabilization in the vorticity equation, Preprint no. 2740, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2740 .
Abstract, PDF (843 kByte)
Discretization of NavierStokes' equations using pressurerobust finite element methods is considered for the high Reynolds number regime. To counter oscillations due to dominating convection we add a stabilization based on a bulk term in the form of a residualbased least squares stabilization of the vorticity equation supplemented by a penalty term on (certain components of) the gradient jump over the elements faces. Since the stabilization is based on the vorticity equation, it is independent of the pressure gradients, which makes it pressurerobust. Thus, we prove pressureindependent error estimates in the linearized case, known as Oseen's problem. In fact, we prove an O(h^{k}+^{1}/2) error estimate in the L^{2}norm that is known to be the best that can be expected for this type of problem. Numerical examples are provided that, in addition to confirming the theoretical results, show that the present method compares favorably to the classical residualbased SUPG stabilization. 
D. Frerichs, Ch. Merdon, Divergencepreserving reconstructions on polygons and a really pressurerobust virtual element method for the Stokes problem, Preprint no. 2683, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2683 .
Abstract, PDF (314 kByte)
Non divergencefree discretisations for the incompressible Stokes problem may suffer from a lack of pressurerobustness characterised by large discretisations errors due to irrotational forces in the momentum balance. This paper argues that also divergencefree virtual element methods (VEM) on polygonal meshes are not really pressurerobust as long as the righthand side is not discretised in a careful manner. To be able to evaluate the righthand side for the testfunctions, some explicit interpolation of the virtual testfunctions is needed that can be evaluated pointwise everywhere. The standard discretisation via an L^{2} bestapproximation does not preserve the divergence and so destroys the orthogonality between divergencefree testfunctions and possibly eminent gradient forces in the righthand side. To repair this orthogonality and restore pressurerobustness another divergencepreserving reconstruction is suggested based on RaviartThomas approximations on local subtriangulations of the polygons. All findings are proven theoretically and are demonstrated numerically in two dimensions. The construction is also interesting for hybrid highorder methods on polygonal or polyhedral meshes. 
G. Fu, Ch. Lehrenfeld, A. Linke, T. Streckenbach, Locking free and gradient robust H(div)conforming HDG methods for linear elasticity, Preprint no. 2680, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2680 .
Abstract, PDF (429 kByte)
Robust discretization methods for (nearlyincompressible) linear elasticity are free of volumelocking and gradientrobust. While volumelocking is a wellknown problem that can be dealt with in many different discretization approaches, the concept of gradientrobustness for linear elasticity is new. We discuss both aspects and propose novel Hybrid Discontinuous Galerkin (HDG) methods for linear elasticity. The starting point for these methods is a divergenceconforming discretization. As a consequence of its wellbehaved Stokes limit the method is gradientrobust and free of volumelocking. To improve computational efficiency, we additionally consider discretizations with relaxed divergenceconformity and a modification which reenables gradientrobustness, yielding a robust and quasioptimal discretization also in the sense of HDG superconvergence.
Vorträge, Poster

C. Cancès, C. ChainaisHillairet, J. Fuhrmann, B. Gaudeul, On four numerical schemes for a unipolar degenerate driftdiffusion model, Finite Volumes for Complex Applications IX (Online Event), Bergen, Norway, June 15  19, 2020.

A. Caiazzo, CFD Simulation for non invasive estimation of blood pressure (online talk), Leibniz MMS Symposium on Computational Geophysics and Fluid Dynamics (Online Event), October 21, 2020, October 21, 2020.

A. Caiazzo, Multiscale modeling of vascularized tissues (online talk), Virtual Physiological Human (VPH2020)  When models, methods & experiments meet the clinic (Online Event), August 24  28, 2020, INRIA, Paris, France, August 28, 2020.

D. Frerichs, A pressurerobust virtual element method for the Stokes problem on polygonal/polyhedral meshes (online talk), Leibniz MMS Symposium on Computational Geophysics and Fluid Dynamics (Online Event), October 21, 2020, October 21, 2020.

D. Frerichs, A really pressurerobust virtual element method for the Stokes problem (online talk), Conference on Scientific Computing (ALGORITMY 2020) (Online Event), September 10  15, 2020, Slovak University of Technology, Podbanské, Slovakia, September 14, 2020.

J. Fuhrmann, D.H. Doan, A. Glitzky, M. Liero, G. Nika, Unipolar driftdiffusion simulation of Sshaped currentvoltage relations for organic semiconductor devices, Finite Volumes for Complex Applications IX (Online Event), Bergen, Norway, June 15  19, 2020.

J. Fuhrmann, C. Guhlke, M. Landstorfer, A. Linke, Ch. Merdon, R. Müller, Quality preserving numerical methods for electroosmotic flow, Einstein Semester on Energybased mathematical methods for reactive multiphase flows: Kickoff Conference (Online Event), October 26  30, 2020.

J. Fuhrmann, Finite volume methods for nonlinear multiphysics Problemp (online talk), VoronoiFVM.jl  finite volume methods for nonlinear multiphysics problems (Online Event), Lisboa, July 31, 2020.

J. Fuhrmann, Quality preserving numerical methods for electroosmotic flow (online talk), Conference on Scientific Computing (ALGORITMY 2020) (Online Event), September 10  15, 2020, Slovak University of Technology, Podbanské, Slovakia, September 14, 2020.

J. Fuhrmann, VTKView.jl  vtk based insitu visualization in Julia (online talk), Julia VizCon (Online Event), March 12  19, 2020, March 15, 2020.

V. John, Algebraic finite element stabilizations for convectiondiffusion equations, Indian Institute of Technology Roorkee, Department of Mathematics, India, January 24, 2020.

V. John, Numerical methods for convectiondominated equations, January 27  30, 2020, Indian Institute of Technology Roorkee, Department of Mathematics, India.

V. John, On the provable convergence order for the kinetic energy of FEMs for the incompressible NavierStokes equations, 7th European Seminar on Computing (ESCO 2020) (Online Event), Pilsen, Czech Republic, June 8  12, 2020.

TH. Koprucki, K. Tabelow, T. Streckenbach, T. Niermann, A. Maltsi, Modelbased geometry reconstruction of TEM images (online poster session), MATH+ Day 2020 (Online Event), November 6, 2020.

A. Linke, Ch. Merdon, On highorder pressurerobust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond, Einstein Semester on Energybased mathematical methods for reactive multiphase flows: Kickoff Conference (Online Event), October 26  30, 2020.

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A. Linke, Gradientrobustness: A new concept assuring accurate spatial discretizations for vectorvalued PDEs, Workshop ``Structure, Regularity and Robustness in the Approximation of PDEs'', Università degli Studi di Milano Statale, Italy, February 10, 2020.

A. Linke, Gradientrobustness: A new concept assuring accurate spatial discretizations for vectorvalued PDEs (online talk), Eindhoven University of Technology, Centre for Analysis, Scientific computing and Applications, Netherlands, June 24, 2020.

A. Linke, On pressurerobust space discretizations and incompressible high Reynolds number flows (online talk), Conference on Scientific Computing (ALGORITMY 2020) (Online Event), September 10  15, 2020, Slovak University of Technology, Podbanské, Slovakia, September 15, 2020.

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CH. Merdon, Gradientrobust discretisations for compressible NavierStokes flows (online talk), Leibniz MMS Symposium on Computational Geophysics and Fluid Dynamics (Online Event), October 21, 2020, October 21, 2020.

CH. Merdon, Wellbalanced discretisation for the compressible Stokes problem by gradientrobustness (online talk), Finite Volumes for Complex Applications IX (Online Event), June 15  19, 2020, University of Bergen, Norway, June 17, 2020.

O. Pártl, Mathematical modeling of nonisothermal compositional compressible fluid flow in zeolite bed and above its surface (online talk), Conference on Scientific Computing (ALGORITMY 2020) (Online Event), September 10  15, 2020, Slovak University of Technology, Podbanské, Slovakia, September 14, 2020.

H. Si, Adaptive exponential time integration of the NavierStokes equations, 3rd AIAA Sonic Boom Prediction Workshop, January 5  10, 2020, American Institute of Aeronautics and Astronautics SciTech Forum, Orlando, Florida, USA, January 10, 2020.

H. Si, On decomposition of embedded prismatoids in $rm I!R^3$ without additional points (online talk), 10th International Conference ``Numerical Geometry, Grid Generation and Scientific Computing'' (NUMGRID 2020) (Online Event), November 25  27, 2020, Russian Academy of Sciences, Federal Research Center of Information and Control, Moscow, Russian Federation, November 27, 2020.
Forschungsgruppen
 Partielle Differentialgleichungen
 Laserdynamik
 Numerische Mathematik und Wissenschaftliches Rechnen
 Nichtlineare Optimierung und Inverse Probleme
 Stochastische Systeme mit Wechselwirkung
 Stochastische Algorithmen und Nichtparametrische Statistik
 Thermodynamische Modellierung und Analyse von Phasenübergängen
 Nichtglatte Variationsprobleme und Operatorgleichungen