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Homepage von Dr. Christian Merdon




Kontakt

Adresse:Weierstraß Institut für Angewandte Analysis und Stochastik
Mohrenstr. 39, 10117 Berlin, Deutschland
Email:Christian.Merdon(at)wias-berlin.de
Phone:+49(0) 30 20372 452
Fax:+49(0) 30 20372 317

Google Scholar
MathSciNet
zbMATH
github

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Kurzer Lebenslauf

seit September 2013 Postdoktorand am Weierstraß-Institut Berlin in der Forschungsgruppe 3 (Numerische Mathematik und Wissenschaftliches Rechnen)
September 2013 Dr. rer. nat. am Institut für Mathematik der Humboldt-Universität zu Berlin
Januar 2011 - August 2013 Wissenschaftlicher Mitarbeiter am Institut für Mathematik der Humboldt-Universität zu Berlin
September 2010 - Dezember 2010 Forschungsaufenthalt an der Yonsei University in Seoul (Republik Korea) mit DAAD Kurzstipendium
Februar 2010 - August 2010 Wissenschaftlicher Mitarbeiter am Institut für Mathematik der Humboldt-Universität zu Berlin
September 2009 - Dezember 2009 Forschungsaufenthalt an der Yonsei University in Seoul (Republik Korea)
Juli 2009 Diplom am Institut für Mathematik der Humboldt-Universität zu Berlin
Mai 2007 - September 2009 Studentische Hilfskraft am Institut für Mathematik der Humboldt-Universität zu Berlin

Interessen- und Forschungsschwerpunkte

  • Finite-Elemente-Methoden
  • Finite-Volumen-Methoden
  • Diffusions-Konvektions-Reaktions-Gleichungen
  • Navier-Stokes-Gleichungen, CFD
  • Elektrochemie
  • (Garantierte) A Posteriori Fehlerkontrolle
  • Hindernisprobleme

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Projekte

  • DFG-Projekt, "Kopplung Atomistischer und Kontinuumsskaliger Modelle der Heterogenen Katalyse mittels eines Reduzierten-Basen-Ansatz und Mehrlevel-On-the-fly-Dünngitter-Interpolation" (zusammen mit Sebastian Matera, Fritz-Haber-Institut) , 2022 - 2024, (Link)
  • Math+ Incubator Project IN-11, "Identifying and Efficiently Computing Band-Edge Energies for Charge Transport Simulations in Strained Materials" (zusammen mit Costanza Manganelli und Patricio Farrell) , 2022-2023, (Link)

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Software


Name Beschreibung
ExtendableGrids.jl
Julia package that offers a container structure for computational grids with lazy creation of adjacencies for finite element and finite volume methods and some basic refinement procedures.
ExtendableFEMBase.jl
Julia package with basis finite element functionalities (basis functions, transformation rules, quadrature formulas, innterpolations, dofmaps...).
ExtendableFEM.jl
Julia package that offers a high level API for finite element methods (based on ExtendableFEMBase.jl and ExtendableGrids.jl) including implementations of pressure-robust and gradient-robust schemes.

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Publikationen


* = Proceedings

Eingereichte/Momentane Arbeiten
[44]
Gradient-robust hybrid DG discretizations for the compressible Stokes equations
P.L. Lederer, C. Merdon
[43]
Augmenting the grad-div stabilization for Taylor--Hood Finite Elements with a Vorticity Stabilization
V. John, C. Merdon, M. Zainelabdeen
2024
[42]
Inf-sup stabilized Scott-Vogelius pairs on general shape-regular simplicial grids for Navier-Stokes equations
N. Ahmed, V. John, X. Li, C. Merdon
CAMWA, accepted (2024)
[41]
An energy-based finite-strain model for 3D heterostructured materials and its validation by curvature analysis
Y. Hadjimichael, C. Merdon, M. Liero, P. Farrell
International Journal for Numerical Methods in Engineering, accepted (2024)
[40]
Pressure-robust L2 error analysis for Raviart--Thomas enriched Scott--Vogelius pairs
V. John, X. Li, C. Merdon
Applied Mathematical Letters, available online (2024)
[39]
Inf-sup stabilized Scott-Vogelius pairs on general simplicial grids by Raviart-Thomas enrichment
V. John, X. Li, C. Merdon and H. Rui
Mathematical Models and Methods in Applied Sciences, Vol. 34, No. 05, pp. 919-949 (2024)
2023
[38*]
Reduced Basis Approach for convection-diffusion equations with non-linear boundary reaction conditions
S. Matera, C. Merdon, D. Runge
Finite Volumes for Complex Applications X - Volume 1, Elliptic and Parabolic Problems FVCA10, Strasbourg, France, October 30, 2023 - November 03, 2023, Invited Contributions
[37]
Pressure-robustness in the context of optimal control
C. Merdon and W. Wollner
SIAM Journal on Control and Optimization 2023 61:1, 342-360
2022
[36]
Guaranteed upper bounds for the velocity error of pressure-robust Stokes discretisations
P.L. Lederer and C. Merdon
Journal of Numerical Mathematics, vol. 30, no. 4, 2022, pp. 267-294 (published online 2021)
[35]
A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes
T. Apel, V. Kempf, A. Linke and C. Merdon
IMA Journal of Numerical Analysis, Volume 42, Issue 1, January 2022, Pages 392-416 (published online 2021)
[34]
Divergence-preserving reconstructions on polygons and a really pressure-robust virtual element method for the Stokes problem
D. Frerichs and C. Merdon
IMA Journal of Numerical Analysis, Volume 42, Issue 1, January 2022, Pages 597-619 (published online 2020)
2021
[33]
A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation
N. Ahmed, G. R. Barrenechea, E. Burman, J. Guzman, A. Linke and C. Merdon
SIAM J. Numer. Anal., 59(5) (2021), 2746--2774
2020
[32*]
Well-Balanced Discretisation for the Compressible Stokes Problem by Gradient-Robustness
A. Linke, C. Merdon
FVCA 2020: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 113--121
[31*]
On the Significance of Pressure-Robustness for the Space Discretization of Incompressible High Reynolds Number Flows
A. Linke, C. Merdon
FVCA 2020: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 103--112
[30]
Pressure-robustness in quasi-optimal a priori estimates for the Stokes problem
A. Linke, C. Merdon and M. Neilan
ETNA, Vol. 52, pp. 281-294
[29]
A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem
M. Akbas, T. Gallouet, A. Gassmann, A. Linke and C. Merdon
Computer Methods in Applied Mechanics and Engineering 367 (2020)
2019
[28]
Models and numerical methods for electrolyte flows
J. Fuhrmann, C. Guhlke, A. Linke, C. Merdon and R. Müller
Models and Numerical Methods for Electrolyte Flows. In: Hintermüller M., Rodrigues J. (eds)
Topics in Applied Analysis and Optimisation. CIM Series in Mathematical Sciences. Springer, Cham (2019)
[27]
Induced charge electroosmotic flow with finite ion size and solvation effects
J. Fuhrmann, C. Guhlke, A. Linke, C. Merdon and R. Müller
Electrochimica Acta 317 (2019), 778--785
[26]
Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods
P. L. Lederer, C. Merdon and J. Schöberl
Numerische Mathematik 142(3) (2019), 713--748
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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Vorträge/Minisymposia

[42] Raviart-Thomas-enriched Scott-Vogelius finite element methods for the Navier-Stokes equations on general meshes , NACONF2023 Glasgow, Scottland (2023-06-28)
[41] Raviart-Thomas enriched Scott-Vogelius finite element methods for the Navier-Stokes equations , GAMM23, Dresden (2023-06-02)
[40] Raviart-Thomas enriched Scott-Vogelius finite element methods for the Navier-Stokes equations , University Twente (SACS Capita Selecta seminar), Enschede, Netherlands (2023-05-10)
[39] Raviart-Thomas enriched Scott-Vogelius finite element methods for the Navier-Stokes equations , City University Hong Kong (online) (2023-01-18)
[38] Recent advances in pressure-robust finite element methods , WCCMAPCOM (online) (2022-08-02)
[37] Recent Advances for pressure-robust Discretisations of the incompressible Navier-Stokes Equations , SIAM AN22 (online) (2022-07-14)
[36] Inf-sup stabilized Scott-Vogelius pairs on general simplicial grids by Raviart-Thomas enrichment , NUM CFD22, WIAS Berlin (2022-07-07)
[M3] Organisator of mini-symposium on 'structure-preserving finite element methods in computational fluid dynamics', ECCOMAS2022, Oslo, Norway (2022-06-08)
[35] A gradient-robust well-balanced scheme for the compressible Navier-Stokes problem, ECCOMAS2022, Oslo, Norway (2022-06-08)
[34] A novel gradient-robust, well-balanced discretisation for the compressible Stokes problem, Leibniz MMS-Days, Potsdam (2022-04-26)
[33] A novel gradient-robust, well-balanced discretisation for the compressible isothermal Navier-Stokes problem, GAMM 91st Annual Meeting (2021-03-18, online)
[32] A gradient-robust discretisation for the compressible Stokes problem, Leibniz MMS-Online Symposium - 1st issue on Computational and Geophysical Fluid Dynamics (2020-10-17, online)
[M2] Organisator of (online) mini-symposium on 'pressure-robust discretisations for flow problems and their applications', ALGORITMY, Podbanske, Slovakia (2020-09-14, online)
[31] A gradient-robust discretisation for the compressible Stokes problem, ALGORITMY, Podbanske, Slovakia (2020-09-14, online)
[30] Well-balanced discretisation for the compressible Stokes problem by gradient-robustness, FVCA9, Bergen, Norway (2020-06-17, online)
[29] A gradient-robust, well-balanced discretisation for the compressible barotropic Stokes problem, ENUMATH2019, Egmond aan Zee, The Netherlands (2019-10-01)
[28] Pressure-robustness in the discretisation of the Navier-Stokes equations, University of Twente, Enschede, The Netherlands (2019-09-30)
[M1] Organisator (together with M. Neilan) of mini-symposium on 'Divergence-free and pressure-robust discretizations for the Navier-Stokes equations', ICIAM2019, Valencia, Spain (2019-07-17)
[27] Pressure-robustness in the discretisation of the Navier-Stokes equations - An overview, ICIAM2019, Valencia, Spain (2019-07-17)
[26] Pressure-robust finite element discretisations for the Navier-Stokes problem , TU Dresden (2019-04-11)
[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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Poster

[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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Vorlesungen

[1] SS 2016 Technische Universität Berlin, Lineare Algebra für Ingenieurwissenschaften
[2] WS 2017/18 Humboldt-Universität zu Berlin, Numerik partieller Differentialgleichungen I
[3] WS 2022/23 Humboldt-Universität zu Berlin, Numerik gewöhnlicher Differentialgleichungen I

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Betreute Aschlussarbeiten

[2] 2023 Masterarbeit Marwa Zainelabdeen Sedahmed Abdelhameed
Freie Universität Berlin (mit Volker John)		 "Pressure- and Convection-Robust Finite Element Discretizations for Flow Problems"
[1] 2019 Masterarbeit Derk Frerichs
Humboldt-Universität zu Berlin		 "Zur Druckrobustheit und Adaptivität einer Virtuellen-Elemente-Methode für das Stokes-Problem"   (pdf)