Christoph Lehrenfeld

Contact

me

Jr.-Prof. Dr. Christoph Lehrenfeld
Institut für Numerische und Angewandte Mathematik
Lotzestraße 16-18
D-37083 Göttingen
Room 104
phone: +49 (0)551 39 10584
fax: +49 (0)551 39 33944
email: lehrenfeld-at-math.uni-goettingen.de



Research interests
  • Numerical methods for PDEs (Finite Elements)
  • Advanced Finite Element Methods:
    • Unfitted Finite Element Methods (XFEM/CutFEM/..)
    • Space-Time Finite Element Methods for evolving domains
    • High Order Finite Element Methods
    • Hybrid Discontinuous Galerkin Methods
  • Applications:
    • fluid dynamics
    • interface problems
    • problems involving moving domains
Short CV
  • Positions
    • 09/2016 - present: Junior professor at University of Göttingen
    • 09/2015 - 08/2016: Postdoctoral Fellow at University of Muenster
    • 03/2015 - 08/2015: Postdoctoral Fellow at TU Wien
    • 10/2010 - 02/2015: Research Associate at RWTH Aachen
    • 06/2010 - 09/2010: Research Associate at TU Wien
  • Education
    • 2010 - 2015: Doctorate in Mathematics at RWTH Aachen
    • 2005 - 2010: Diploma in Computational Engineering Science at RWTH Aachen
Publications
Recent publications

recent

[1] Philip L. Lederer, Christoph Lehrenfeld, and Joachim Schöberl. Hybrid discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. part ii. arXiv preprint arXiv:1805.06787, 2018. [ bib | http | .pdf ]
[2] Christoph Lehrenfeld and Stephan Rave. Mass conservative reduced order modeling of a free boundary osmotic cell swelling problem. arXiv preprint arXiv:1805.01812, 2018. [ bib | http | .pdf ]
[3] Philipp W. Schroeder, Volker John, Philip L. Lederer, Christoph Lehrenfeld, Gert Lube, and Joachim Schöberl. On reference solutions and the sensitivity of the 2d Kelvin--Helmholtz instability problem. arXiv preprint arXiv:1803.06893, 2018. [ bib | http | .pdf ]
[4] Christoph Lehrenfeld and Maxim A. Olshanskii. An Eulerian finite element method for PDEs in time-dependent domains. arXiv preprint arXiv:1803.01779, 2018. [ bib | http | .pdf ]
[5] Fabian Heimann and Christoph Lehrenfeld. Numerical integration on hyperrectangles in isoparametric unfitted finite elements. accepted for publication in Proceedings of ENUMATH 2017, 2017. [ bib ]
[6] Christoph Lehrenfeld, Maxim A. Olshanskii, and Xianmin Xu. A stabilized trace finite element method for partial differential equations on evolving surfaces. arXiv preprint arXiv:1709.07117, accepted for publication in SIAM Journal on Numerical Analysis, 2017. [ bib | http | .pdf ]
[7] Philip L. Lederer, Christoph Lehrenfeld, and Joachim Schöberl. Hybrid discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. part i. arXiv preprint arXiv:1707.02782, accepted for publication in SIAM Journal on Numerical Analysis, 2017. [ bib | http | .pdf ]

Journal publications

journal

[1] Frits de Prenter, Christoph Lehrenfeld, and André Massing. A note on the penalty parameter in Nitsche's method for unfitted boundary value problems. Computers and Mathematics with Applications, available online 12 April 2018, 2018. [ bib | DOI | http | .pdf ]
[2] Philipp W. Schroeder, Alexander Linke, Christoph Lehrenfeld, and Gert Lube. Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier-Stokes equations. SeMA Journal, pages 1--25, April 2018. [ bib | DOI | http ]
[3] Guosheng Fu and Christoph Lehrenfeld. A strongly conservative hybrid DG/mixed FEM for the coupling of Stokes and Darcy flow. Journal of Scientific Computing, Mar 2018. [ bib | DOI | http ]
[4] Christoph Lehrenfeld and Arnold Reusken. L2-estimates for a high order unfitted finite element method for elliptic interface problems. Journal of Numerical Mathematics, 00:--, 2018. first online. [ bib | DOI | http | .pdf ]
[5] Jörg Grande, Christoph Lehrenfeld, and Arnold Reusken. Analysis of a high-order trace finite element method for PDEs on level set surfaces. SIAM Journal on Numerical Analysis, 56(1):228--255, 2018. [ bib | http | .pdf ]
[6] Christoph Lehrenfeld and Arnold Reusken. Analysis of a high order unfitted finite element method for an elliptic interface problem. IMA J. Numer. Anal., 00:1--37, 2017. first online. [ bib | DOI | http | .pdf ]
[7] Christoph Lehrenfeld and Arnold Reusken. Optimal preconditioners for Nitsche-XFEM discretizations of interface problems. Numerische Mathematik, 135:313--332, 2017. [ bib ]
[8] Christoph Lehrenfeld and Joachim Schöberl. High order exactly divergence-free hybrid discontinuous Galerkin methods for unsteady incompressible flows. Computer Methods in Applied Mechanics and Engineering, 307:339 -- 361, 2016. [ bib | DOI | http | .pdf ]
[9] Christoph Lehrenfeld. High order unfitted finite element methods on level set domains using isoparametric mappings. Computer Methods in Applied Mechanics and Engineering, 300:716 -- 733, 2016. [ bib | DOI | http | .pdf ]
[10] Carlos J. Falconi D., Christoph Lehrenfeld, Holger Marschall, Christoph Meyer, R. Abiev, Dieter Bothe, Arnold Reusken, Michael Schlüter, and Martin Wörner. Numerical and experimental analysis of local flow phenomena in laminar Taylor flow in a square mini-channel. Physics of Fluids, 28(1), 2016. [ bib | DOI | http ]
[11] Christoph Lehrenfeld. The Nitsche XFEM-DG space-time method and its implementation in three space dimensions. SIAM J. Sci. Comp., 37(1):A245--A270, 2015. [ bib | DOI | http | .pdf ]
[12] Holger Marschall, Stephan Boden, Christoph Lehrenfeld, Carlos J. Falconi D., Uwe Hampel, Arnold Reusken, Martin Wörner, and Dieter Bothe. Validation of interface capturing and tracking techniques with different surface tension treatments against a Taylor bubble benchmark problem. Computers & Fluids, 102:336 -- 352, 2014. [ bib | DOI | http ]
[13] Christoph Lehrenfeld and Arnold Reusken. Analysis of a Nitsche XFEM-DG discretization for a class of two-phase mass transport problems. SIAM J. Numer. Anal., 51:958--983, 2013. [ bib | DOI | http | .pdf ]
[14] Christoph Lehrenfeld and Arnold Reusken. Nitsche-XFEM with streamline diffusion stabilization for a two-phase mass transport problem. SIAM J. Sci. Comp., 34:2740--2759, 2012. [ bib | DOI | http | .pdf ]

Book chapters

bookchap

[1] Christoph Lehrenfeld. A higher order isoparametric fictitious domain method for level set domains. In Stéphane P. A. Bordas, Erik Burman, Mats G. Larson, and Maxim A. Olshanskii, editors, Geometrically Unfitted Finite Element Methods and Applications, pages 65--92. Springer International Publishing, 2017. [ bib | DOI ]
[2] Holger Marschall, Carlos Falconi, Christoph Lehrenfeld, Rufat Abiev, Martin Wörner, Arnold Reusken, and Dieter Bothe. Direct numerical simulations of Taylor bubbles in a square mini-channel: Detailed shape and flow analysis with experimental validation. In Transport Processes at Fluidic Interfaces, pages 663--679. Springer, 2017. [ bib ]
[3] Christoph Lehrenfeld and Arnold Reusken. High order unfitted finite element methods for interface problems and PDEs on surfaces. In Transport Processes at Fluidic Interfaces, pages 33--63. Springer, 2017. [ bib | .pdf ]
[4] Christoph Lehrenfeld and Arnold Reusken. Finite element techniques for the numerical simulation of two-phase flows with mass transport. In Computational Methods for Complex Liquid-Fluid Interfaces, pages 353--372, 2015. [ bib | .pdf ]
[5] Joachim Schöberl and Christoph Lehrenfeld. Domain decomposition preconditioning for high order hybrid discontinuous Galerkin methods on tetrahedral meshes. In Thomas Apel and Olaf Steinbach, editors, Advanced Finite Element Methods and Applications, volume 66 of Lecture Notes in Applied and Computational Mechanics, pages 27--56. Springer Berlin Heidelberg, 2013. [ bib | DOI | http | .pdf ]
[6] Christoph Koutschan, Christoph Lehrenfeld, and Joachim Schöberl. Computer algebra meets finite elements: An efficient implementation for Maxwells equations. In Numerical and Symbolic Scientific Computing, volume 1 of Texts and Monographs in Symbolic Computation, pages 105--121. Springer Vienna, 2012. [ bib | DOI | .pdf ]

Prooceding articles

proc

[1] Philip L. Lederer, Carl-Martin Pfeiler, Christoph Wintersteiger, and Christoph Lehrenfeld. Higher order unfitted FEM for Stokes interface problems. PAMM, 16(1):7--10, 2016. [ bib | DOI | http ]
[2] Christoph Lehrenfeld. Removing the stabilization parameter in fitted and unfitted symmetric Nitsche formulations. In Proc. of ECCOMAS 2016, 2016. [ bib | .pdf ]
[3] Sebastian Aland, Christoph Lehrenfeld, Holger Marschall, Christoph Meyer, and Stephan Weller. Accuracy of two-phase flow simulations: The Taylor flow benchmark. Proc. Appl. Math. Mech., 13(1):595--598, December 2013. [ bib | DOI | http ]
[4] Christoph Lehrenfeld. Nitsche-XFEM for a transport problem in two-phase incompressible flows. PAMM, 11(1):613--614, December 2011. [ bib | DOI | http ]

Theses

theses

[1] Christoph Lehrenfeld. On a Space-Time Extended Finite Element Method for the Solution of a Class of Two-Phase Mass Transport Problems. PhD thesis, RWTH Aachen, February 2015. [ bib | http | .pdf ]
[2] Christoph Lehrenfeld. Hybrid Discontinuous Galerkin Methods for Incompressible Flow Problems. Master's thesis, RWTH Aachen, May 2010. [ bib | .pdf ]

Teaching
  • SS 18 (University of Göttingen)
    • Scientific computing with partial differential equations
    • (Ober)Seminar on Numerical Methods for PDEs (joint with Prof. Lube)
  • WS 17/18 (University of Göttingen)
    • Seminar on Numerics of partial differential equations
    • (Ober)Seminar on Numerical Methods for PDEs (joint with Prof. Lube)
  • SS 17 (University of Göttingen)
    • Numerics of partial differential equations
    • (Ober)Seminar on Numerical Methods for PDEs (joint with Prof. Lube)
  • WS 16/17 (University of Göttingen)
    • Advanced Finite Elements
    • (Ober)Seminar on Numerical Methods for PDEs (joint with Prof. Lube)
  • SS 16 (WWU Münster)
    • Numerical methods for PDEs II
    • Seminar on Numerical Methods in Biological and Medical Sciences
  • WS 15/16 (WWU Münster)
    • Numerical methods for PDEs I
    • Practicals to Numerical methods for PDEs I
    • Introduction to programming with Python
  • SS 15 (TU Wien)
    • Extended Finite Element Methods
  • WS 14/15 (RWTH Aachen)
    • Seminar on Numerical Analysis
  • SS 13 (RWTH Aachen)
    • Numerical Mathematics for Mech. Engineers
  • WS 10/11 (RWTH Aachen)
    • C++-Course
  • SS 09 (RWTH Aachen)
    • Advanced Finite Element Methods
  • SS 08 (RWTH Aachen)
    • "Mathematische Grundlagen II" (CES)
Software
  • Netgen/NGSolve is a mesh generator and a high performance multiphysics finite element software that I mainly work this
  • ngsxfem is an Add-On library to Netgen/NGSolve which add the essential features to implement geometrically unfitted FEM
  • ngsxfem-jupyter contains several tutorials to get started with ngsxfem
Media
  • You can find some simulation videos on youtube
About this document
Author Christoph Lehrenfeld (lehrenfeld-at-math.uni-goettingen.de)
Date 2018-06-18 09:35:08