Homepage of Dr. Christian Merdon




Contact

Address:Weierstrass Institute for Applied Analysis and Stochastics
Mohrenstr. 39, 10117 Berlin, Germany
Email:Christian.Merdon(at)wias-berlin.de
Phone:+49(0) 30 20372 452
Fax:+49(0) 30 20372 317


Google Scholar
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Short CV

since September 2013 Postdoc at the Weierstraß Institute Berlin
September 2013 Dr. rer. nat. at the Department of Mathematics of the Humboldt-Universität zu Berlin
January 2011 - August 2013 Research Assistant at the Department of Mathematics of the Humboldt-Universität zu Berlin
September 2010 - December 2010 Research stay at the Yonsei University in Seoul (Republic Korea) with DAAD scholarship
February 2010 - August 2010 Research Assistant at the Department of Mathematics of the Humboldt-Universität zu Berlin
September 2009 - December 2009 Research stay at the Yonsei University in Seoul (Republic Korea)
July 2009 Diploma at the Department of Mathematics of the Humboldt-Universität zu Berlin
May 2007 - September 2009 Student Assistant at the Department of Mathematics of the Humboldt-Universität zu Berlin

Fields of Interest and Research

  • Finite Element Methods
  • Finite Volume Methods
  • Diffusion-Convection-Reaction Equations
  • Navier-Stokes Equations, CFD
  • Electrochemistry
  • (Guaranteed) Error Control
  • Obstacle Problems

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Publications


* = Proceedings

Current Submissions and Projects
Induced charge electroosmotic flow with finite ion size and solvation effects
J. Fuhrmann, C. Guhlke, A. Linke, C. Merdon and R. Müller
(submitted on 2019-01-21)
Models and numerical methods for electrolyte flows
J. Fuhrmann, C. Guhlke, A. Linke, C. Merdon and R. Müller
(submitted on 2018-07-24)
Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods
P. L. Lederer, C. Merdon and J. Schöberl
(submitted on 2017-12-05, accepted by Numerische Mathematik on 2018-11-05)
2018
[25]
Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes problem
A. Linke, C. Merdon, M. Neilan and F. Neumann
Mathematics of Computations 87 (2018), 1543--1566
[24]
On really locking-free mixed finite element methods for the transient incompressible Stokes equations
N. Ahmed, A. Linke and C. Merdon
SIAM J. Numer. Anal., 56(1) (2018), 185--209
[23]
Towards pressure-robust mixed methods for the incompressible Navier--Stokes equations
N. Ahmed, A. Linke and C. Merdon
Computational Methods in Applied Mathematics 18(3) (2018), 353--372
2017
[22]
On the divergence constraint in mixed finite element methods for incompressible flows
V. John, A. Linke, C. Merdon, M. Neilan and L. Rebholz
SIAM Review 59(3) (2017), 492--544
[21]
Divergence-free reconstruction operators for pressure-robust Stokes discretizations with continuous pressure finite elements
P. Lederer, A. Linke, C. Merdon and J. Schöberl
SIAM J. Numer. Anal. 55(3) (2017), 1291--1314
[20]
Optimal L2 velocity error estimate for a modified pressure-robust Crouzeix--Raviart Stokes element
A. Linke, C. Merdon and W. Wollner
IMA J. Numer. Anal. 37(1) (2017), 354--374
2016
[19]
Local equilibration error estimators for guaranteed error control in adaptive higher-order stochastic Galerkin finite element methods
M. Eigel and C. Merdon
SIAM/ASA J. Uncertainty Quantification 4(1) (2016), 1372--1397
[18]
An adaptive multi level Monte-Carlo method with stochastic bounds for quantities of interest with uncertain data
M. Eigel, C. Merdon and J. Neumann
SIAM/ASA J. Uncertainty Quantification 4(1) (2016), 1219--1245
[17]
Pressure-robustness and discrete Helmholtz projectors in mixed finite element methods for the incompressible Navier--Stokes equations
A. Linke and C. Merdon
Computer Methods in Applied Mechanics and Engineering 311 (2016), 304--326
[16]
Inverse modeling of thin layer flow cells for detection of solubility, transport and reaction coefficients from experimental data
H. Baltruschat, J. Fuhrmann, M. Khodayari, A. Linke, C. Merdon, F. Neumann and T. Streckenbach
Electrochimica Acta 211 (2016), 1--10
[15]
On velocity errors due to irrotational forces in the Navier--Stokes momentum balance
A. Linke and C. Merdon
J. Comput. Phys. 313 (2016), 654--661
[14]
Determining solubility and diffusivity using a flow cell coupled to mass spectrometer
M. Khodayari, P. Reinsberg, A.A. Abd-El-Latif, C. Merdon, J. Fuhrmann and H. Baltruschat
Chemphyschem 17 (2016), no. 11, 1647--1655
[13]
Guaranteed error control for the pseudostress approximation of the Stokes equations
P. Bringmann, C. Carstensen and C. Merdon
Numer. Methods Partial Differential Eqs 32 (2016), no. 5, 1411--1432
[12]
Equilibration a posteriori error estimation for convection-diffusion-reaction problems
M. Eigel and C. Merdon
Journal of Scientific Computing 67 (2016), no. 2, 747--768
2015
[11]
Guaranteed energy error estimators for a modified robust Crouzeix-Raviart Stokes element
A. Linke and C. Merdon
Journal of Scientific Computing 64 (2015), no. 2, 541--558
[10]
Optimal and pressure-independent L^2 velocity error estimates for a modified Crouzeix-Raviart Stokes element with BDM reconstructions
C. Brennecke, A. Linke, C. Merdon and J. Schöberl
J. Comput. Math. 33 (2015), no. 2
2014
[9*]
Coupling of Fluid Flow and Solute Transport Using a Divergence-Free Reconstruction of the Crouzeix-Raviart Element
J. Fuhrmann, A. Linke and C. Merdon
FVCA 7, Finite Volumes for Complex Applications VII, Berlin, June 15-20, 2014, Springer Proceedings in Mathematics & Statistics, 587--595
[8]
Refined fully explicit a posteriori residual-based error control
C. Carstensen and C. Merdon
SIAM J. Numer. Anal. 52 (2014), no. 4, 1709--1728
[7]
Computational survey on a posteriori error estimators for the Crouzeix-Raviart nonconforming finite element methods for the Stokes problem
C. Carstensen and C. Merdon
Comput. Methods Appl. Math. 14 (2014), no. 1, 35--54
2013
[PhD]
Aspects of guaranteed error control in computations for partial differential equations
C. Merdon
Ph.D. Thesis (submitted on 2013-02-28, defense on 2013-08-02, publication on 2013-09-17)
[6*]
Aspects of guaranteed error control in CPDEs
C. Carstensen, C. Merdon and J. Neumann
Springer Proceedings in Mathematics and Statistics 45 (2013), 103--119
[5]
Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem
C. Carstensen and C. Merdon
J. Comput. Appl. Math. 249 (2013), 74--94
[4]
Effective postprocessing for equilibration a posteriori error estimators
C. Carstensen and C. Merdon
Numer. Math. 123 (2013), no. 3, 425--459
[3]
A posteriori error estimator competition for conforming obstacle problems
C. Carstensen and C. Merdon
Numer. Methods Partial Differential Equations 29 (2013), no. 2, 667--692
2011
[2*]
Remarks on the state of the art of a posteriori error control of elliptic PDEs in energy norms in practise
C. Carstensen and C. Merdon
Stud. Univ. Babeş-Bolyai Math. 56 (2011), no. 2, 273--293
2010
[1]
Estimator competition for Poisson problems
C. Carstensen and C. Merdon
J. Comput. Math. 28 (2010), no. 3, 309--330
2009
[Dip]
A posteriori Fehlerschätzer für elliptische partielle Differentialgleichungen
C. Merdon
Diplomarbeit (2009)

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Talks

[25] Pressure-robust mixed finite element methods and refined a posteriori error control for the Stokes problem, Universität Göttingen (2019-01-29)
[24] Well-balanced discretisation for the compressible Stokes problem, VMS2018, Berlin (2018-12-06)
[23] Pressure-robust finite element methods for the Navier-Stokes equations, GAMM Workshop on Numerical Analysis, Aachen (2017-11-02)
[22] Pressure-robust mixed finite element methods for the Navier-Stokes equations, RMMM8, Berlin (2017-08-02)
[21] Pressure-robustness in mixed finite element discretisations for the Navier-Stokes equations, Universtität des Saarlandes (2017-07-12)
[20] Druckrobuste Finite-Elemente-Methoden für die Navier-Stokes-Gleichungen, Universtität Paderborn (2017-04-25)
[19] A novel concept for the discretisation of the coupled Nernst-Planck-Poisson-Navier-Stokes system, MODVAL14, Karlsruhe (2017-03-03)
[18] Pressure-robust mixed finite element methods for transient Navier--Stokes discretisations, TU Wien (2016-12-14)
[17] Pressure-robust finite element methods for the Navier--Stokes equations and mass-conservative coupling to transport processes, FAU Erlangen-Nürnberg (2016-05-11)
[16] Pressure-Robust 1st and 2nd-Order Finite Element Methods for Navier-Stokes Discretisations, NoKo 2016, Uni Lübeck (2016-04-22)
[15] Inverse Modelling of Transport and Reaction Processes in Thin-Layer Flow Cells, MODVAL13, Lausanne, Suisse (2016-03-23)
[14] Pressure-Robust 1st and 2nd Order Finite Element Methods for Navier-Stokes Discretisations, VMS2016, Magdeburg (2016-03-17)
[13] Pressure-Robust Finite Element Methods for Navier-Stokes Discretisations, WIAS Berlin (2016-01-21)
[12] A Modified Pressure-Robust 2nd-Order Finite Element Method for Navier-Stokes Discretisations, 28th FEM-Symposium, Chemnitz (2015-09-28)
[11] 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 in Saint-Malo, France (2015-06-01)
[10] A Modified Robust Crouzeix-Raviart FEM for the Stokes Problem, Research Seminar HU Berlin (2015-01-14)
[9] Aspects of Guaranteed Error Control for Finite Element Approximations in Computations for PDEs, WIAS Berlin (2013-07-10)
[8] Garantierte Fehlerkontrolle bei PDGLen mit aktuellen Equilibrierungstechniken, WIAS Berlin (2013-04-02)
[7] Guaranteed Error Control in CPDE, Eccomas 2012 at University of Vienna, Austria (2012-09-11)
[6] Improved Explicit Residual-Based A Posteriori Error Control, Research Seminar HU Berlin (2012-05-16)
[5] A posteriori Fehlerschätzer für elliptische partielle Differentialgleichungen in Energienormen, Workshop über Kontaktmechanik und adaptive FEM im SPP 1480, TU Dortmund (2011-10-05)
[4] A Posteriori Error Estimator Competition for Elliptic PDEs in Energy Norms, Research Seminar HU Berlin (2011-02-02)
[3] A Posteriori Error Estimator Competition for 2nd-order PDEs, Research Seminar HU Berlin (2010-06-02)
[2] Series of talks on FEM in 10 Lines of Matlab, Adaptive Mesh Refinement for FEM and Obstacle Problems, Yonsei University, Seoul, Republic of Korea (2009-11-09)
[1] Estimator Competition, Research Seminar HU Berlin (2008-11-16)

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Posters

[4] [3] [2] [1]
[5] C. 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, ISE 67th Annual Meeting (2016-08-24)
[4] A. Linke, C. Merdon, Pressure-Robustness and Acceleration of Navier--Stokes Solvers, MMS Days 2016 (2016-01-27), (pdf)
[3] J. Fuhrmann, A. Linke, C. Merdon, M. Khodayari, H. Baltruschat, Detection of Solubility, Transport and Reaction Coefficients from Experimental Data by Inverse Modeling of Thin Layer Flow Cells, ISE Lausanne (2014-09-03), (pdf)
[2] J. Fuhrmann, A. Linke, C. Merdon, Coupling of Fluid Flow and Solute Transport Using a Divergence-Free Reconstruction of the Crouzeix-Raviart Element, FVCA7 Berlin (2014-06-17), (pdf)
[1] C. Merdon, A Posteriori Error Estimation for Elliptic PDEs in Energy Norms, Yonsei University Seoul (2010-10-23), (pdf)

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Lectures

[1] SS 2016 Technische Universität Berlin, Lineare Algebra für Ingenieurwissenschaften
[2] WS 2017/18 Humboldt-Universität zu Berlin, Numerik partieller Differentialgleichungen I