journal.bib
@article{LR_SISC_2012,
title = {{Nitsche-XFEM} with streamline diffusion stabilization for a two-phase mass transport problem},
author = {Christoph Lehrenfeld and Arnold Reusken},
journal = {SIAM J. Sci. Comp.},
volume = {34},
pages = {2740--2759},
year = {2012},
publisher = {SIAM},
url = {http://epubs.siam.org/doi/abs/10.1137/110855235},
doi = {http://dx.doi.org/10.1137/110855235},
pdf = {https://www.igpm.rwth-aachen.de/Download/reports/reusken/ARpaper62.pdf}
}
@article{LR_SINUM_2013,
author = {Lehrenfeld, Christoph and Reusken, Arnold},
title = {Analysis of a {Nitsche XFEM-DG} Discretization for a class of Two-Phase Mass Transport Problems},
journal = {SIAM J. Numer. Anal.},
year = {2013},
volume = {51},
pages = {958--983},
file = {reuskenlehrenfeld13.pdf},
doi = {10.1137/120875260},
url = {http://epubs.siam.org/doi/abs/10.1137/120875260},
pdf = {https://www.igpm.rwth-aachen.de/Download/reports/reusken/ARpaper67.pdf}
}
@article{MBLFHRWB_CF_2014,
title = {Validation of Interface Capturing and Tracking techniques with different surface tension treatments against a {Taylor} bubble benchmark problem },
author = {Holger Marschall and Stephan Boden and Christoph Lehrenfeld and Carlos J. Falconi D. and Uwe Hampel and Arnold Reusken and Martin W\"{o}rner and Dieter Bothe},
journal = {Computers \& Fluids },
volume = {102},
number = {},
pages = {336 - 352},
year = {2014},
note = {},
issn = {0045-7930},
doi = {http://dx.doi.org/10.1016/j.compfluid.2014.06.030},
url = {http://www.sciencedirect.com/science/article/pii/S0045793014002771}
}
@article{L_SISC_2015,
title = {The {Nitsche} {XFEM-DG} space-time method and its implementation in three space dimensions},
author = {Lehrenfeld, Christoph},
journal = {SIAM J. Sci. Comp.},
volume = {37},
number = {1},
pages = {A245--A270},
year = {2015},
publisher = {SIAM},
doi = {http://dx.doi.org/10.1137/130943534},
url = {http://epubs.siam.org/doi/abs/10.1137/130943534},
pdf = {https://arxiv.org/pdf/1408.2941v1.pdf}
}
@article{FLMMABRSW_POF_2016,
author = {Carlos J. Falconi D. and Christoph Lehrenfeld and Holger Marschall and Christoph Meyer and R. Abiev and Dieter Bothe and Arnold Reusken and Michael Schl\"{u}ter and Martin W\"{o}rner},
title = {Numerical and experimental analysis of local flow phenomena in laminar {Taylor} flow in a square mini-channel},
journal = {Physics of Fluids},
year = {2016},
volume = {28},
number = {1},
eid = 012109,
pages = {},
url = {http://scitation.aip.org/content/aip/journal/pof2/28/1/10.1063/1.4939498},
doi = {http://dx.doi.org/10.1063/1.4939498}
}
@article{L_CMAME_2016,
title = {High order unfitted finite element methods on level set domains using isoparametric mappings },
author = {Christoph Lehrenfeld},
journal = {Computer Methods in Applied Mechanics and Engineering },
volume = {300},
number = {},
pages = {716 -- 733},
year = {2016},
note = {},
issn = {0045-7825},
doi = {http://dx.doi.org/10.1016/j.cma.2015.12.005},
url = {http://www.sciencedirect.com/science/article/pii/S0045782515004004},
pdf = {https://arxiv.org/pdf/1509.02762v1.pdf}
}
@article{LS_CMAME_2016,
title = {High order exactly divergence-free Hybrid Discontinuous {Galerkin} Methods for unsteady incompressible flows },
author = {Christoph Lehrenfeld and Joachim Schöberl},
journal = {Computer Methods in Applied Mechanics and Engineering },
volume = {307},
number = {},
pages = {339 -- 361},
year = {2016},
note = {},
issn = {0045-7825},
doi = {http://dx.doi.org/10.1016/j.cma.2016.04.025},
url = {http://www.sciencedirect.com/science/article/pii/S004578251630264X},
pdf = {https://arxiv.org/pdf/1508.04245v2.pdf}
}
@article{L_NM_2017,
title = {Optimal preconditioners for {Nitsche-XFEM} discretizations of interface problems},
author = {Lehrenfeld, Christoph and Reusken, Arnold},
journal = {Numerische Mathematik},
volume = {135},
pages = {313-332},
year = {2017},
publisher = {Springer}
}
@article{LR_IMAJNA_2018,
title = {Analysis of a high order unfitted finite element method for an elliptic interface problem},
author = {Lehrenfeld, Christoph and Reusken, Arnold},
journal = {IMA J. Numer. Anal.},
url = {https://academic.oup.com/imajna/article-abstract/doi/10.1093/imanum/drx041/4084723/Analysis-of-a-highorder-unfitted-finite-element},
pdf = {https://arxiv.org/pdf/1602.02970.pdf},
volume = {38},
issue = {3},
pages = {1351--1387},
doi = {10.1093/imanum/drx041},
year = {2018}
}
@article{grande2018analysis,
title = {Analysis of a High-Order Trace Finite Element Method for {PDE}s on Level Set Surfaces},
author = {Grande, J{\"o}rg and Lehrenfeld, Christoph and Reusken, Arnold},
journal = {SIAM Journal on Numerical Analysis},
volume = {56},
number = {1},
pages = {228--255},
year = {2018},
publisher = {SIAM},
url = {http://epubs.siam.org/doi/abs/10.1137/16M1102203},
pdf = {https://arxiv.org/pdf/1611.01100.pdf}
}
@article{LR_JNMA_2018,
title = {{$L^2$}-estimates for a high order unfitted finite element method for elliptic interface problems},
author = {Lehrenfeld, Christoph and Reusken, Arnold},
journal = {Journal of Numerical Mathematics},
url = {https://www.degruyter.com/view/j/jnma.just-accepted/jnma-2017-0109/jnma-2017-0109.xml?format=INT},
pdf = {https://arxiv.org/pdf/1604.04529.pdf},
note = {first online},
volume = {00},
pages = {--},
doi = {10.1515/jnma-2017-0109},
year = {2018}
}
@article{FL_JSC_2018,
author = {Fu, Guosheng and Lehrenfeld, Christoph},
title = {A Strongly Conservative Hybrid {DG}/Mixed {FEM} for the Coupling of {Stokes} and {Darcy} Flow},
journal = {Journal of Scientific Computing},
volume = {77},
issue = {3},
pages = {1605--1620},
issn = {1573-7691},
doi = {10.1007/s10915-018-0691-0},
url = {https://doi.org/10.1007/s10915-018-0691-0}
}
@article{SLLL_SEMA_2018,
title = {Towards computable flows and robust estimates for inf-sup stable {FEM} applied to the time-dependent incompressible {Navier-Stokes} equations},
author = {Schroeder, Philipp W. and Linke, Alexander and Lehrenfeld, Christoph and Lube, Gert},
journal = {SeMA Journal},
doi = {10.1007/s40324-018-0157-1},
year = {2018},
month = {April},
day = {13},
volume = {75},
number = {4},
pages = {629--653},
doi = {10.1007/s40324-018-0157-1},
url = {https://doi.org/10.1007/s40324-018-0157-1}
}
@article{dPLM_CAMWA_2017,
title = {A note on the penalty parameter in {Nitsche's} method for unfitted boundary value problems},
author = {de Prenter, Frits and Lehrenfeld, Christoph and Massing, Andr{\'e}},
journal = {Computers and Mathematics with Applications},
year = {2018},
volume = {75},
issue = {12},
pages = {4322--4336},
issn = {0898-1221},
doi = {https://doi.org/10.1016/j.camwa.2018.03.032},
url = {http://www.sciencedirect.com/science/article/pii/S0898122118301688},
pdf = {https://arxiv.org/pdf/1709.05832.pdf}
}
@article{LLS_SIAM_2017,
title = {Hybrid Discontinuous {Galerkin} methods with relaxed {H(div)}-conformity for incompressible flows. Part I},
author = {Lederer, Philip L. and Lehrenfeld, Christoph and Sch{\"o}berl, Joachim},
journal = {SIAM J. Numer. Anal.},
year = {2018},
volume = {56},
issue = {4},
pages = {2070--2094},
doi = {10.1137/17M1138078},
notes = { NAM preprint 2017-05},
url = {https://arxiv.org/abs/1707.02782},
pdf = {https://arxiv.org/pdf/1707.02782.pdf}
}
@article{LOX_SIAM_2017,
title = {A stabilized trace finite element method for partial differential equations on evolving surfaces},
author = {Lehrenfeld, Christoph and Olshanskii, Maxim A. and Xu, Xianmin},
journal = {SIAM J. Numer. Anal.},
year = {2018},
volume = {56},
issue = {3},
pages = {1643--1672},
doi = {10.1137/17M1148633},
url = {https://arxiv.org/abs/1709.07117},
pdf = {https://arxiv.org/pdf/1709.07117.pdf}
}
@article{SJLLLS_CAMWA_2019,
title = {On reference solutions and the sensitivity of the {2D} {Kelvin--Helmholtz} instability problem},
author = {Schroeder, Philipp W. and John, Volker and Lederer, Philip L. and Lehrenfeld, Christoph and Lube, Gert and Schöberl, Joachim},
journal = {Computers \& Mathematics with Applications},
volume = {77},
number = {4},
pages = {1010--1028},
year = {2019},
publisher = {Elsevier},
video = {https://www.youtube.com/watch?v=xtBK8U4dOvg}
}
@article{LLS_ESAIM_2019,
title = {Hybrid Discontinuous {Galerkin} methods with relaxed {H(div)}-conformity for incompressible flows. Part II},
author = {Lederer, Philip L. and Lehrenfeld, Christoph and Sch{\"o}berl, Joachim},
journal = {ESAIM: M2AN},
year = {2019},
volume = {53},
pages = {503--522},
doi = {10.1051/m2an/2018054},
notes = { NAM preprint 2017-05},
url = {https://arxiv.org/abs/1805.06787},
pdf = {https://arxiv.org/pdf/1805.06787.pdf}
}
@article{LO_ESAIM_2019,
title = {An {Eulerian} Finite Element Method for {PDE}s in time-dependent domains},
author = {Lehrenfeld, Christoph and Olshanskii, Maxim A.},
journal = {ESAIM: M2AN},
year = {2019},
volume = {53},
pages = {585--614},
doi = {10.1051/m2an/2018068},
url = {https://arxiv.org/abs/1803.01779},
pdf = {https://arxiv.org/pdf/1803.01779.pdf}
}
@article{LR_ACOM_2019,
title = {Mass conservative reduced order modeling of a free boundary osmotic cell swelling problem},
author = {Lehrenfeld, Christoph and Rave, Stephan},
journal = {Advances in Computational Mathematics},
pages = {1--25},
year = {2018},
publisher = {Springer},
code = {https://zenodo.org/record/2539712},
url = {https://link.springer.com/article/10.1007/s10444-019-09691-z},
pdf = {https://arxiv.org/pdf/1805.01812.pdf}
}
@article{vWRLHM_CF_2019,
title = {Numerical benchmarking of fluid-rigid body interactions},
author = {von Wahl, Henry and Richter, Thomas and Lehrenfeld, Christoph and Heiland, Jan and Minakowski, Piotr},
journal = {Computers \& Fluids},
pages = {104290},
year = {2019},
publisher = {Elsevier},
url = {https://doi.org/10.1016/j.compfluid.2019.104290},
code = {https://zenodo.org/record/3253455},
keywords = {Benchmarking, Computational fluid dynamics, Fluid–structure interaction, Finite elements, Code validation, Reference values}
}
@article{FKLLS_IJNMF_2019,
title = {High-order {DG} solvers for under-resolved turbulent incompressible flows: A comparison of {L2} and {H(div)} methods},
author = {Fehn, Niklas and Kronbichler, Martin and Lehrenfeld, Christoph and Lube, Gert and Schroeder, Philipp W.},
journal = {International Journal for Numerical Methods in Fluids},
volume = {91},
number = {11},
pages = {533-556},
keywords = {discontinuous Galerkin, high-order finite elements, incompressible Navier-Stokes equations, Taylor-Green vortex, turbulent channel flow, underresolved turbulent flows},
doi = {10.1002/fld.4763},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.4763},
year = {2019},
pdf = {https://arxiv.org/pdf/1905.00142.pdf}
}
@article{LLS_IJNME_2019,
title = {Divergence-free tangential finite element methods for incompressible flows on surfaces},
author = {Lederer, Philip L. and Lehrenfeld, Christoph and Sch\"{o}berl, Joachim},
volume = {121},
number = {11},
pages = {2503-2533},
keywords = {divergence-conforming finite elements, incompressible Navier-Stokes equations, Piola transformation, surface PDEs, tangential vector field},
doi = {10.1002/nme.6317},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6317},
year = {2020},
code = {https://zenodo.org/record/3406173},
eprint = {1909.06229},
archiveprefix = {arXiv},
pdf = {https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.6317}
}
@article{PHL_ARXIV_2020,
title = {Sweeping preconditioners for stratified media in the presence of reflections},
author = {Janosch Preuß and Thorsten Hohage and Christoph Lehrenfeld},
journal = {Springer Nature Partial Differential Equations and Applications},
keywords = {Helmholtz equation, Dirichlet-to-Neumann operator, Preconditioning, Domain decomposition, High-frequency waves, Computational seismology, Perfectly matched layers, Sweeping preconditioner},
volume = {1},
issue = {17},
year = {2020},
eprint = {2002.12016},
archiveprefix = {arXiv},
primaryclass = {math.NA},
doi = {10.1007/s42985-020-00019-x},
url = {https://link.springer.com/article/10.1007/s42985-020-00019-x},
pdf = {https://link.springer.com/content/pdf/10.1007/s42985-020-00019-x.pdf},
code = {https://zenodo.org/record/3686802}
}
@article{FLLS_ARXIV_2020,
title = {Locking free and gradient robust {H(div)}-conforming {HDG} methods for linear elasticity},
author = {Guosheng Fu and Christoph Lehrenfeld and Alexander Linke and Timo Streckenbach},
journal = {Journal of Scientific Computing},
keywords = {linear elasticity, nearly incompressible, locking phenomenon, volumelocking, gradient-robustness, Discontinuous Galerkin, H(div)-conforming HDG methods},
year = {2021},
issue = {86},
number = {39},
eprint = {2001.08610},
archiveprefix = {arXiv},
primaryclass = {math.NA},
url = {https://link.springer.com/article/10.1007/s10915-020-01396-6},
doi = {https://doi.org/10.1007/s10915-020-01396-6},
pdf = {https://arxiv.org/pdf/2001.08610.pdf}
}
@article{IMAJNA_vWRL_2021,
author = {von Wahl, Henry and Richter, Thomas and Lehrenfeld, Christoph},
title = {An unfitted {Eulerian} finite element method for the time-dependent {Stokes} problem on moving domains},
journal = {IMA Journal of Numerical Analysis},
year = {2021},
month = {07},
issn = {0272-4979},
doi = {10.1093/imanum/drab044},
url = {https://doi.org/10.1093/imanum/drab044},
code = {https://zenodo.org/record/3647571},
pdf = {https://arxiv.org/pdf/2002.02352.pdf},
eprint = {https://academic.oup.com/imajna/advance-article-pdf/doi/10.1093/imanum/drab044/38864286/drab044.pdf}
}
@article{JOSS_LHPvW_2021,
doi = {10.21105/joss.03237},
url = {https://doi.org/10.21105/joss.03237},
year = {2021},
publisher = {The Open Journal},
volume = {6},
number = {64},
pages = {3237},
author = {Christoph Lehrenfeld and Fabian Heimann and Janosch Preuß and Henry von Wahl},
title = {\texttt{ngsxfem}: Add-on to {NGSolve} for geometrically unfitted finite element discretizations},
keywords = {numerical software, open source software, NGSolve, unfitted FEM, level set geometries, space-time, higher order FEM},
code = {https://github.com/ngsxfem/ngsxfem},
journal = {Journal of Open Source Software}
}
@article{HLP2021,
title = {Learned infinite elements},
author = {Thorsten Hohage and Christoph Lehrenfeld and Janosch Preu\ss},
year = {2021},
journal = {SIAM J. Sci. Comput.},
volume = {43},
number = {5},
pages = {A3552-A3579},
doi = {10.1137/20M1381757},
code = {https://doi.org/10.25625/XPLPRR},
keywords = {transparent boundary conditions, Dirichlet-to-Neumann map, helioseismology, learning, infinite elements, rational approximation, Helmholtz equation}
}
@article{Stocker_JOSS_2022,
doi = {10.21105/joss.04135},
url = {https://doi.org/10.21105/joss.04135},
year = {2022},
publisher = {The Open Journal},
volume = {7},
number = {71},
pages = {4135},
author = {Paul Stocker},
title = {\texttt{NGSTrefftz}: Add-on to {NGSolve} for {Trefftz} methods},
keywords = {numerical software, open source software, NGSolve, Trefftz DG, higher order FEM},
code = {https://github.com/PaulSt/ngstrefftz},
journal = {Journal of Open Source Software}
}
@article{LL_SINUM_2022,
title = {Isoparametric unfitted {BDF} -- Finite element method for {PDEs} on evolving domains},
author = {Yimin Lou and Christoph Lehrenfeld},
journal = {SIAM Journal on Numerical Analysis},
volume = {60},
number = {4},
pages = {2069-2098},
year = {2022},
doi = {10.1137/21M142126X},
url = {https://doi.org/10.1137/21M142126X},
pdf = {https://arxiv.org/pdf/2105.09162.pdf},
code = {https://gitlab.gwdg.de/lehrenfeld/repro-isop-unf-bdf-fem},
keywords = {Eulerian time stepping, isoparametric FEM, unfitted FEM, evolving domains,ghost penalty, stabilization, higher order FEM, BDF, projection errors}
}
@article{HLP2023,
title = {{Geometrically Higher Order Unfitted Space-Time Methods for PDEs on Moving Domains}},
author = {Fabian Heimann and Christoph Lehrenfeld and Janosch Preu\ss{}},
journal = {SIAM Journal on Scientific Computing},
volume = {45},
number = {2},
pages = {B139-B165},
year = {2023},
doi = {10.1137/22M1476034},
url = {https://doi.org/10.1137/22M1476034},
pdf = {https://arxiv.org/pdf/2202.02216.pdf},
code = {https://gitlab.gwdg.de/fabian.heimann/repro-ho-unf-space-time-fem},
keywords = {Unfitted FEM, Space-Time FEM, Isoparametric Unfitted FEM, Higher order FEM, Petrov-Galerkin, Galerkin Collocation, }
}
@article{LS_IJNME_2023,
title = {Embedded {Trefftz Discontinuous Galerkin} methods},
author = {Christoph Lehrenfeld and Paul Stocker},
journal = {International Journal for Numerical Methods in Engineering},
volume = {124},
number = {17},
pages = {3637--3661},
year = {2023},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.7258},
pdf = {https://arxiv.org/pdf/2201.07041.pdf},
code = {https://github.com/PaulSt/NGSTrefftz},
keywords = {Trefftz DG methods, Embedded Trefftz DG methods},
doi = {10.1002/nme.7258}
}
@article{HLSvW_M2AN_2023,
doi = {10.1051/m2an/2023064},
author = {Heimann, Fabian and Lehrenfeld, Christoph and Stocker, Paul and von Wahl, Henry},
keywords = {Numerical Analysis (math.NA), Unfitted FEM, Trefftz DG, Aggregated FEM},
title = {{Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems}},
journal = {ESAIM: M2AN},
year = {2023},
month = {September},
volume = {57},
number = {5},
pages = {2803--2833},
url = {https://doi.org/10.1051/m2an/2023064},
pdf = {https://www.esaim-m2an.org/articles/m2an/pdf/2023/05/m2an220275.pdf},
code = {https://doi.org/10.5281/zenodo.7474688},
video = {http://www.birs.ca/events/2024/5-day-workshops/24w5218/videos/watch/202405141000-Lehrenfeld.html}
}
@article{MARDI,
doi = {10.4171/MAG/152},
url = {https://euromathsoc.org/magazine/articles/152},
author = {Boege, Tobias and Fritze, René and Görgen, Christiane and Hanselman, Jeroen and Iglezakis, Dorothea and Kastner, Lars and Koprucki, Thomas and Krause, Tabea and Lehrenfeld, Christoph and Polla, Silvia and Reidelbach, Marco and Riedel, Christian and Saak, Jens and Schembera, Björn and Tabelow, Karsten and Weber, Marcus},
keywords = {History and Overview (math.HO), FOS: Mathematics, FOS: Mathematics},
title = {{Research-Data Management Planning in the German Mathematical Community}},
publisher = {},
journal = {Eur. Math. Soc. Mag.},
issue = {130},
pages = {40--47},
year = {2023},
pdf = {https://arxiv.org/pdf/2211.12071.pdf},
copyright = {Creative Commons Attribution Share Alike 4.0 International},
entrysubtype = {own}
}
@article{LLS_NM_2024,
doi = {10.1007/s00211-024-01404-z},
title = {{Trefftz Discontinuous Galerkin discretization for the Stokes problem}},
author = {Philip L. Lederer and Christoph Lehrenfeld and Paul Stocker},
journal = {Numerische Mathematik},
year = {2024},
issue = {},
pages = {},
eprint = {2306.14600},
archiveprefix = {arXiv},
primaryclass = {math.NA},
url = {https://link.springer.com/content/pdf/10.1007/s00211-024-01404-z.pdf},
pdf = {https://link.springer.com/content/pdf/10.1007/s00211-024-01404-z.pdf},
code = {https://doi.org/10.25625/UHPEQG},
keywords = {Trefftz-DG, Stokes}
}
@article{LvBV_MC_2024,
title = {Analysis of divergence-preserving unfitted finite element methods for the mixed {P}oisson problem},
author = {Christoph Lehrenfeld and Tim van Beeck and Igor Voulis},
journal = {Math. Comp.},
doi = {10.1090/mcom/4027},
year = {2024},
issue = {},
pages = {},
eprint = {2306.12722},
archiveprefix = {arXiv},
primaryclass = {math.NA},
url = {https://www.ams.org/journals/mcom/0000-000-00/S0025-5718-2024-04027-9/viewer/#info},
pdf = {https://doi.org/10.1090/mcom/4027},
code = {https://doi.org/10.25625/LYR2CG},
keywords = {unfitted FEM, mixed FEM, divergence-preserving FEM, mixed Poisson problem}
}
@article{HL_IMAJNA_2025,
title = {Geometry Error Analysis of a parametric mapping for Higher Order Unfitted Space-Time Methods},
author = {Fabian Heimann and Christoph Lehrenfeld},
year = {2025},
journal = {IMA Journal of Numerical Analysis},
doi = {10.1093/imanum/drae098},
issue = {00},
pages = {1--55},
eprint = {2311.02348},
archiveprefix = {arXiv},
primaryclass = {math.NA},
url = {https://academic.oup.com/imajna/advance-article/doi/10.1093/imanum/drae098/8068555},
pdf = {https://academic.oup.com/imajna/advance-article-pdf/doi/10.1093/imanum/drae098/62366016/drae098.pdf},
keywords = {unfitted FEM, space-time, geometry error analysis}
}