Prof. Dr. Christoph Lehrenfeld

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  • 2024 | Preprint
    ​ ​Geometrically Higher Order Unfitted Space-Time Methods for PDEs on Moving Domains: Geometry Error Analysis​
    Heimann, F.  & Lehrenfeld, C. ​ (2024)
    ​Details  arXiv 
  • 2024 | Preprint
    ​ ​LiveDocs: Crafting Interactive Development Environments From Research Findings​
    Costa Klein, P. ; Lehrenfeld, C. ; Osterhoff, M.  & Uecker, M. ​ (2024). DOI: https://doi.org/10.48550/ARXIV.2402.09475 
    ​Details  DOI  arXiv 
  • 2023 | Lecture
    ​ ​Slides for the CRC 1456 Research Retreat Session "Live-Docs and RDM: Reproducibility and beyond"​
    Costa Klein, P.; Lehrenfeld, C.  & Osterhoff, M.​ (2023)
    CRC 1456 Retreat; 2023-11-15​, Hofgeismar. DOI: https://doi.org/10.25625/PVFHWA 
    ​Details  DOI 
  • 2023 | Journal Article | Research Paper
    ​ ​Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems​
    Heimann, F. ; Lehrenfeld, C. ; Stocker, P. & von Wahl, H.​ (2023) 
    Mathematical Modelling and Numerical Analysis, 57(5) pp. 2803​-2833​.​ DOI: https://doi.org/10.1051/m2an/2023064 
    ​Details  DOI  arXiv 
  • 2023 | Preprint | 
    ​ ​Trefftz Discontinuous Galerkin discretization for the Stokes problem​
    Lederer, P. L.; Lehrenfeld, C.  & Stocker, P.​ (2023)
    ​Details  arXiv 
  • 2023 | Preprint | 
    ​ ​Analysis of divergence-preserving unfitted finite element methods for the mixed Poisson problem​
    Lehrenfeld, C. ; van Beeck, T.& Voulis, I. ​ (2023)
    ​Details  arXiv 
  • 2023 | Journal Article
    ​ ​Geometrically Higher Order Unfitted Space-Time Methods for PDEs on Moving Domains​
    Heimann, F. ; Lehrenfeld, C.   & Preuß, J.​ (2023) 
    SIAM Journal on Scientific Computing, 45(2) pp. B139​-B165​.​ DOI: https://doi.org/10.1137/22M1476034 
    ​Details  DOI  arXiv 
  • 2023 | Journal Article | Research Paper | 
    ​ ​Embedded Trefftz discontinuous Galerkin methods​
    Lehrenfeld, C.   & Stocker, P.​ (2023) 
    International Journal for Numerical Methods in Engineering,.​
    ​Details  arXiv 
  • 2023 | Journal Article | 
    ​ ​Embedded Trefftz discontinuous Galerkin methods​
    Lehrenfeld, C.   & Stocker, P.​ (2023) 
    International Journal for Numerical Methods in Engineering, art. nme.7258​.​ DOI: https://doi.org/10.1002/nme.7258 
    ​Details  DOI 
  • 2023 | Journal Article
    ​ ​Research-Data Management Planning in the German Mathematical Community​
    Boege, T.; Fritze, R.; Görgen, C.; Hanselman, J.; Iglezakis, D.; Kastner, L. & Koprucki, T. et al.​ (2023) 
    EMS magazine, 130 pp. 40​-47​.​
    ​Details  arXiv 
  • 2023 | Research Data
    ​ ​Correlations of solar oscillations: modeling and inversions (LiveDoc)​
    Van Beeck, T.& Lehrenfeld, C. ​ (2023)
    ​GRO.data. DOI: https://doi.org/10.25625/IZZ529 
    ​Details  DOI 
  • 2022 | Preprint
    ​ ​A new T-compatibility condition and its application to the discretization of the damped time-harmonic Galbrun's equation​
    Halla, M. ; Lehrenfeld, C.  & Stocker, P.​ (2022)
    ​Details  arXiv 
  • 2022 | Research Data
    ​ ​Replication Data for: Robust finite element discretizations for a simplified Galbrun's equation​
    Alemán, T.; Halla, M. ; Lehrenfeld, C.  & Stocker, P.​ (2022)
    ​Göttingen Research Online / Data. DOI: https://doi.org/10.25625/9VR9WT 
    ​Details  DOI 
  • 2022 | Journal Article
    ​ ​Isoparametric Unfitted BDF--Finite Element Method for PDEs on Evolving Domains​
    Lou, Y. & Lehrenfeld, C. ​ (2022) 
    SIAM Journal on Numerical Analysis, 60(4) pp. 2069​-2098​.​ DOI: https://doi.org/10.1137/21M142126X 
    ​Details  DOI 
  • 2022 | Other Publication Type | 
    ​ ​Data policy for CRC 1456​
    Lehrenfeld, C. ; Hohage, T. ; Uecker, M. ; Henne, T. ; Holme, H. C. M.  & Rügge, C. ​ (2022)
    ​Göttingen: ​GRO.data. DOI: https://doi.org/10.25625/42GS0I 
    ​Details  DOI 
  • 2022 | Conference Paper
    ​ ​Robust finite element discretizations for a simplified Galbrun's equation​
    Aleman, T.; Halla, M. ; Lehrenfeld, C.   & Stocker, P.​ (2022)
    ​8th European Congress on Computational Methods in Applied Sciences and Engineering​, Oslo.
    Scipedia. DOI: https://doi.org/10.23967/eccomas.2022.206 
    ​Details  DOI  arXiv 
  • 2021 | Journal Article
    ​ ​An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains​
    von Wahl, H.; Richter, T. & Lehrenfeld, C. ​ (2021) 
    IMA Journal of Numerical Analysis,.​ DOI: https://doi.org/10.1093/imanum/drab044 
    ​Details  DOI 
  • 2021 | Software
    ​ ​ngsxfem​ 2.0​
    Lehrenfeld, Christoph; Heimann, Fabian; Preuß, Janosch; von Wahl, Henry  (2021) DOI: https://doi.org/10.5281/zenodo.5081123 
    ​Details  DOI 
  • 2021 | Research Data
    ​ ​Replication Data for: Learned infinite elements​
    Hohage, T. ; Lehrenfeld, C.  & Preuß, J.​ (2021)
    ​Göttingen Research Online / Data. DOI: https://doi.org/10.25625/XPLPRR 
    ​Details  DOI 
  • 2021 | Lecture
    ​ ​Slides of the RDM Workshop for the CRC1456 from 2021-06-21 and 2021-06-28​
    Gnadt, T.; Uecker, M.; Lehrenfeld, C. ; Rügge, C.& Holme, H. C. M.​ (2021)
    RDM Workshop for the CRC1456 2021; 2021​, Göttingen. DOI: https://doi.org/10.25625/MIWPNO 
    ​Details  DOI 
  • 2021 | Journal Article
    ​ ​Locking-Free and Gradient-Robust ${\varvec{H}}({{\,\mathrm{{\text {div}}}\,}})$-Conforming HDG Methods for Linear Elasticity​
    Fu, G.; Lehrenfeld, C. ; Linke, A. & Streckenbach, T.​ (2021) 
    Journal of Scientific Computing, 86(3).​ DOI: https://doi.org/10.1007/s10915-020-01396-6 
    ​Details  DOI 
  • 2021 | Journal Article | 
    ​ ​ngsxfem: Add-on to NGSolve for geometrically unfitted finite element discretizations​
    Lehrenfeld, C. ; Heimann, F.; Preuß, J. & von Wahl, H.​ (2021) 
    The Journal of Open Source Software, 6(64).​ DOI: https://doi.org/10.21105/joss.03237 
    ​Details  DOI 
  • 2020 | Journal Article | Research Paper | 
    ​ ​Learned infinite elements​
    Hohage, T. ; Lehrenfeld, C.   & Preuß, J.​ (2020) 
    SIAM Journal on Scientific Computing, 43(5) pp. A3552​-A3579​.​ DOI: https://doi.org/10.1137/20M1381757 
    ​Details  DOI 
  • 2020 | Journal Article | 
    ​ ​Divergence-free tangential finite element methods for incompressible flows on surfaces​
    Lederer, P. L.; Lehrenfeld, C.   & Schöberl, J.​ (2020) 
    International Journal for Numerical Methods in Engineering, 121(11) pp. 2503​-2533​.​ DOI: https://doi.org/10.1002/nme.6317 
    ​Details  DOI  arXiv 
  • 2020 | Journal Article | Research Paper | 
    ​ ​Sweeping preconditioners for stratified media in the presence of reflections​
    Preuß, J.; Hohage, T.   & Lehrenfeld, C. ​ (2020) 
    Partial Differential Equations and Applications, 1(4).​ DOI: https://doi.org/10.1007/s42985-020-00019-x 
    ​Details  DOI 
  • 2019 | Journal Article
    ​ ​Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. Part II​
    Lederer, P. L.; Lehrenfeld, C.   & Schöberl, J.​ (2019) 
    European Series in Applied and Industrial Mathematics. Proceedings and Surveys, 53(2) pp. 503​-522​.​ DOI: https://doi.org/10.1051/m2an/2018054 
    ​Details  DOI 
  • 2019 | Journal Article
    ​ ​Mass Conservative Reduced Order Modeling of a Free Boundary Osmotic Cell Swelling Problem​
    Lehrenfeld, C.   & Rave, S.​ (2019) 
    Advances in Computational Mathematics, 45(5-6) pp. 2215​-2239​.​ DOI: https://doi.org/10.1007/s10444-019-09691-z 
    ​Details  DOI  arXiv 
  • 2019 | Journal Article
    ​ ​L2-error analysis of an isoparametric unfitted finite element method for elliptic interface problems​
    Lehrenfeld, C.   & Reusken, A.​ (2019) 
    Journal of Numerical Mathematics, 27(2) pp. 85​-99​.​ DOI: https://doi.org/10.1515/jnma-2017-0109 
    ​Details  DOI 
  • 2019 | Journal Article
    ​ ​Numerical benchmarking of fluid-rigid body interactions​
    Wahl, H. von; Richter, T.; Lehrenfeld, C. ; Heiland, J. & Minakowski, P.​ (2019) 
    Computers & Fluids, 193 art. 104290​.​ DOI: https://doi.org/10.1016/j.compfluid.2019.104290 
    ​Details  DOI  arXiv 
  • 2019 | Journal Article
    ​ ​Viscous dissipation in DG methods for turbulent incompressible flows​
    Lehrenfeld, C. ; Lube, G.   & Schröder, P. W. ​ (2019) 
    Proceedings in Applied Mathematics and Mechanics, 19(1).​ DOI: https://doi.org/10.1002/pamm.201900049 
    ​Details  DOI 
  • 2019 | Journal Article
    ​ ​An Eulerian finite element method for PDEs in time-dependent domains​
    Lehrenfeld, C.   & Olshanskii, M.​ (2019) 
    European Series in Applied and Industrial Mathematics. Proceedings and Surveys, 53(2) pp. 585​-614​.​ DOI: https://doi.org/10.1051/m2an/2018068 
    ​Details  DOI 
  • 2019 | Journal Article | 
    ​ ​High-order DG solvers for under-resolved turbulent incompressible flows: A comparison of $L^2$ and $H(div)$ methods​
    Fehn, N.; Kronbichler, M.; Lehrenfeld, C. ; Lube, G.   & Schröder, P. W. ​ (2019) 
    International Journal for Numerical Methods in Fluids, 91(11) pp. 533​-556​.​ DOI: https://doi.org/10.1002/fld.4763 
    ​Details  DOI  arXiv 
  • 2019 | Book Chapter
    ​ ​Numerical Integration on Hyperrectangles in Isoparametric Unfitted Finite Elements​
    Heimann, F.& Lehrenfeld, C. ​ (2019)
    In:​Radu, Florin Adrian; Kumar, Kundan; Berre, Inga; Nordbotten, Jan Martin; Pop, Iuliu Sorin​ (Eds.), Numerical Mathematics and Advanced Applications ENUMATH 2017 pp. 193​-202. (Vol. 126). ​Cham: ​Springer International Publishing. DOI: https://doi.org/10.1007/978-3-319-96415-7_16 
    ​Details  DOI 
  • 2018 | Journal Article | Research Paper
    ​ ​On reference solutions and the sensitivity of the 2D Kelvin-Helmholtz instability problem​
    Schröder, P. W. ; John, V.; Lederer, P. L.; Lehrenfeld, C. ; Lube, G.   & Schöberl, J.​ (2018) 
    Computers & Mathematics with Applications, 77(4) pp. 1010​-1028​.​ DOI: https://doi.org/10.1016/j.camwa.2018.10.030 
    ​Details  DOI  arXiv 
  • 2018 | Book Chapter
    ​ ​A Higher Order Isoparametric Fictitious Domain Method for Level Set Domains​
    Lehrenfeld, C. ​ (2018)
    In:​Bordas, Stéphane P. A.; Burman, Erik; Larson, Mats G.; Olshanskii, Maxim A.​ (Eds.), Geometrically Unfitted Finite Element Methods and Applications pp. 65​-92. (Vol. 121). ​Cham: ​Springer International Publishing. DOI: https://doi.org/10.1007/978-3-319-71431-8 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​A Strongly Conservative Hybrid DG/Mixed FEM for the Coupling of Stokes and Darcy Flow​
    Fu, G. & Lehrenfeld, C. ​ (2018) 
    Journal of Scientific Computing, 77(3) pp. 1605​-1620​.​ DOI: https://doi.org/10.1007/s10915-018-0691-0 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​Analysis of a high-order unfitted finite element method for elliptic interface problems​
    Lehrenfeld, C.   & Reusken, A.​ (2018) 
    IMA Journal of Numerical Analysis, 38(3) pp. 1351​-1387​.​ DOI: https://doi.org/10.1093/imanum/drx041 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​Hybrid Discontinuous Galerkin Methods with Relaxed H(div)-Conformity for Incompressible Flows. Part I​
    Lederer, P. L.; Lehrenfeld, C.   & Schöberl, J.​ (2018) 
    SIAM Journal on Numerical Analysis, 56(4) pp. 2070​-2094​.​ DOI: https://doi.org/10.1137/17M1138078 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier–Stokes equations​
    Schröder, P. W. ; Lehrenfeld, C. ; Linke, A. & Lube, G. ​ (2018) 
    SeMA Journal, 75(4) pp. 629​-653​.​ DOI: https://doi.org/10.1007/s40324-018-0157-1 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​Analysis of a High-Order Trace Finite Element Method for PDEs on Level Set Surfaces​
    Grande, J.; Lehrenfeld, C.   & Reusken, A.​ (2018) 
    SIAM Journal on Numerical Analysis, 56(1) pp. 228​-255​.​ DOI: https://doi.org/10.1137/16M1102203 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​A Stabilized Trace Finite Element Method for Partial Differential Equations on Evolving Surfaces​
    Lehrenfeld, C. ; Olshanskii, M. A. & Xu, X.​ (2018) 
    SIAM Journal on Numerical Analysis, 56(3) pp. 1643​-1672​.​ DOI: https://doi.org/10.1137/17M1148633 
    ​Details  DOI 
  • 2017 | Book Chapter
    ​ ​Direct numerical simulations of Taylor bubbles in a square mini-channel: Detailed shape and flow analysis with experimental validation​
    Marschall, H.; Falconi, C.; Lehrenfeld, C. ; Abiev, R.; Wörner, M.; Reusken, A.& Bothe, D.​ (2017)
    In: Transport Processes at Fluidic Interfaces pp. 663​-679. ​Springer.
    ​Details 
  • 2017 | Journal Article
    ​ ​Higher order unfitted finite element methods for interface problems​
    Lehrenfeld, C. ​ (2017) 
    Oberwolfach Reports, 6.​
    ​Details 
  • 2017 | Book Chapter
    ​ ​High order unfitted finite element methods for interface problems and PDEs on surfaces​
    Lehrenfeld, C.  & Reusken, A.​ (2017)
    In: Transport Processes at Fluidic Interfaces pp. 33​-63. ​Springer.
    ​Details 
  • 2017 | Journal Article
    ​ ​A note on the penalty parameter in Nitsche's method for unfitted boundary value problems​
    de Prenter, F.; Lehrenfeld, C.   & Massing, A.​ (2017) 
    Computers & Mathematics with Applications, 75(12) pp. 4322​-4336​.​ DOI: https://doi.org/10.1016/j.camwa.2018.03.032 
    ​Details  DOI  arXiv 
  • 2016 | Report
    ​ ​Removing the stabilization parameter in fitted and unfitted symmetric Nitsche formulations​
    Lehrenfeld, C. ​ (2016). DOI: https://doi.org/10.7712/100016 
    ​Details  DOI  arXiv 
  • 2016 | Journal Article
    ​ ​Numerical and experimental analysis of local flow phenomena in laminar Taylor flow in a square mini-channel​
    Falconi, C. J.; Lehrenfeld, C. ; Marschall, H.; Meyer, C.; Abiev, R.; Bothe, D. & Reusken, A. et al.​ (2016) 
    Physics of Fluids, 28(1) art. 012109​.​ DOI: https://doi.org/10.1063/1.4939498 
    ​Details  DOI 
  • 2016 | Journal Article
    ​ ​Optimal preconditioners for Nitsche-XFEM discretizations of interface problems​
    Lehrenfeld, C.   & Reusken, A.​ (2016) 
    Numerische Mathematik, 135(2) pp. 313​-332​.​ DOI: https://doi.org/10.1007/s00211-016-0801-6 
    ​Details  DOI 
  • 2016 | Journal Article
    ​ ​Higher order unfitted FEM for Stokes interface problems​
    Lederer, P.; Pfeiler, C.-M.; Wintersteiger, C. & Lehrenfeld, C. ​ (2016) 
    Proceedings in Applied Mathematics and Mechanics, 16(1) pp. 7​-10​.​ DOI: https://doi.org/10.1002/pamm.201610003 
    ​Details  DOI 
  • 2015 | Book Chapter
    ​ ​Finite element techniques for the numerical simulation of two-phase flows with mass transport​
    Lehrenfeld, C.  & Reusken, A.​ (2015)
    In: Computational Methods for Complex Liquid-Fluid Interfaces pp. 353​-372. 
    ​Details 
  • 2015 | Thesis | Doctoral Thesis
    ​ ​On a Space-Time Extended Finite Element Method for the Solution of a Class of Two-Phase Mass Transport Problems​
    Lehrenfeld, C. ​ (2015)
    RWTH Aachen. 
    ​Details 
  • 2015 | Journal Article
    ​ ​High order exactly divergence-free Hybrid Discontinuous Galerkin Methods for unsteady incompressible flows​
    Lehrenfeld, C.   & Schöberl, J.​ (2015) 
    Computer Methods in Applied Mechanics and Engineering, 307 pp. 339​-361​.​ DOI: https://doi.org/10.1016/j.cma.2016.04.025 
    ​Details  DOI  arXiv 
  • 2015 | Journal Article
    ​ ​High order unfitted finite element methods on level set domains using isoparametric mappings​
    Lehrenfeld, C. ​ (2015) 
    Computer Methods in Applied Mechanics and Engineering, 300 pp. 716​-733​.​ DOI: https://doi.org/10.1016/j.cma.2015.12.005 
    ​Details  DOI  arXiv 
  • 2014 | Journal Article
    ​ ​Validation of Interface Capturing and Tracking techniques with different surface tension treatments against a Taylor bubble benchmark problem​
    Marschall, H.; Boden, S.; Lehrenfeld, C. ; Falconi D., C. J.; Hampel, U.; Reusken, A. & Wörner, M. et al.​ (2014) 
    Computers & Fluids, 102 pp. 336​-352​.​ DOI: https://doi.org/10.1016/j.compfluid.2014.06.030 
    ​Details  DOI 
  • 2014 | Journal Article
    ​ ​The Nitsche XFEM-DG space-time method and its implementation in three space dimensions​
    Lehrenfeld, C. ​ (2014) 
    SIAM Journal on Scientific Computing, 37(1) pp. A245​-A270​.​ DOI: https://doi.org/10.1137/130943534 
    ​Details  DOI  arXiv 
  • 2013 | Book Chapter
    ​ ​Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes​
    Schöberl, J.& Lehrenfeld, C. ​ (2013)
    In:​Apel, T.; Steinbach, O.​ (Eds.), Advanced Finite Element Methods and Applications pp. 27​-56. (Vol. 66).  DOI: https://doi.org/10.1007/978-3-642-30316-6_2 
    ​Details  DOI 
  • 2013 | Journal Article
    ​ ​Analysis of a Nitsche XFEM-DG Discretization for a Class of Two-Phase Mass Transport Problems​
    Lehrenfeld, C.   & Reusken, A.​ (2013) 
    SIAM Journal on Numerical Analysis, 51(2) pp. 958​-983​.​ DOI: https://doi.org/10.1137/120875260 
    ​Details  DOI 
  • 2013 | Journal Article
    ​ ​Accuracy of two-phase flow simulations: The Taylor Flow benchmark​
    Aland, S.; Lehrenfeld, C. ; Marschall, H.; Meyer, C.   & Weller, S.​ (2013) 
    Proceedings in Applied Mathematics and Mechanics, 13(1) pp. 595​-598​.​ DOI: https://doi.org/10.1002/pamm.201310278 
    ​Details  DOI 
  • 2012 | Journal Article
    ​ ​Nitsche-XFEM with Streamline Diffusion Stabilization for a Two-Phase Mass Transport Problem​
    Lehrenfeld, C.   & Reusken, A.​ (2012) 
    SIAM Journal on Scientific Computing, 34(5) pp. A2740​-A2759​.​ DOI: https://doi.org/10.1137/110855235 
    ​Details  DOI 
  • 2011 | Book Chapter
    ​ ​Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwell's Equations​
    Koutschan, C.; Lehrenfeld, C.  & Schoeberl, J.​ (2011)
    In:​Langer, Ulrich​ (Ed.), Numerical and symbolic scientific computing: progress and prospects pp. 105​-121.  DOI: https://doi.org/10.1007/978-3-7091-0794-2_6 
    ​Details  DOI  arXiv 
  • 2011 | Journal Article
    ​ ​Nitsche-XFEM for a transport problem in two-phase incompressible flows​
    Lehrenfeld, C. ​ (2011) 
    Proceedings in Applied Mathematics and Mechanics, 11(1) pp. 613​-614​.​ DOI: https://doi.org/10.1002/pamm.201110296 
    ​Details  DOI 
  • 2010 | Thesis | Diploma Thesis
    ​ ​Hybrid Discontinuous Galerkin Methods for Incompressible Flow Problems​
    Lehrenfeld, C. ​ (2010)
    RWTH Aachen.  DOI: https://doi.org/10.25625/O4VBYH 
    ​Details  DOI 

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