@Online{SR22,
  author      = {H. Sass and A. Reusken},
  date        = {2022-12-22},
  title       = {An Accurate and Robust Eulerian Finite Element Method for Partial Differential Equations on Evolving Surfaces},
  eprint      = {2212.12030},
  eprintclass = {math.NA},
  eprinttype  = {arXiv}, 
}

@Article{HLSvW22,
  author           = {Heimann, F. and Lehrenfeld, C. and Stocker, P. and von Wahl, H.},
  date             = {2023-09-14},
  journaltitle     = {ESAIM Math. Model. Numer. Anal.},
  title            = {Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems},
  doi              = {10.1051/m2an/2023064},
  number           = {5},
  pages            = {2803--2833},
  volume           = {57},
  publisher        = {{EDP} Sciences},
}

@Dataset{HLSvW22b,
  author    = {F. Heimann and C. Lehrenfeld and P. Stocker and H. von Wahl},
  date      = {2022-12},
  title     = {Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems - Reproduction scripts},
  doi       = {10.5281/zenodo.7474688},
  location  = {Zenodo repository},
}

@Article{vWW22,
  author           = {von Wahl, H. and Wick, T.},
  date             = {2023-10-01},
  journaltitle     = {Comput. Methods Appl. Mech. Engrg.},
  title            = {A high-accuracy framework for phase-field fracture interface reconstructions with application to Stokes fluid-filled fracture surrounded by an elastic medium},
  doi              = {10.1016/j.cma.2023.116202},
  pages            = {116202},
  volume           = {415},
  publisher        = {Elsevier {BV}},
}

@Dataset{vWW22b,
  author      = {H. von Wahl and T. Wick},
  date        = {2022-12-15},
  title       = {A high-precision framework for phase-field fracture interface reconstructions with application to Stokes fluid-filled fracture surrounded by an elastic medium - Reproduction code},
  doi         = {10.5281/zenodo.7443025},
  location    = {Zenodo repository},
}

@Article{vWR21a,
  author       = {von Wahl, H. and Richter, T.},
  date         = {2021-11-10},
  title        = {Error analysis for a parabolic {PDE} model problem on a coupled moving domain in a fully {E}ulerian framework},
  journaltitle = {SIAM J. Numer. Anal.},
  doi          = {10.1137/21M1458417},
  eprint       = {2111.05607},
  eprintclass  = {math.NA},
  eprinttype   = {arXiv},
}

@Dataset{vWR21b,
  author    = {von Wahl, H. and Richter, T.},
  date      = {2021},
  title     = {Error analysis for a parabolic PDE model problem on a coupled moving domain in a fully Eulerian framework - Reproduction Scripts},
  doi       = {10.5281/zenodo.6505243},
  location  = {Zenodo repository},
}

@InProceedings{vWR23,
  author    = {H. von Wahl and T. Richter},
  booktitle = {Proc. Appl. Math. Mech.},
  date      = {2023},
  title     = {An {Eulerian} time-stepping scheme for a coupled parabolic moving domain problem using equal order unfitted finite elements},
  doi       = {10.1002/pamm.202200003},
}

@PhDThesis{Lui22,
  author      = {H. Liu},
  date        = {2022},
  institution = {University of Pittsburgh},
  title       = {Unfitted finite element methods for the Stokes problem using the Scott-Vogelius pair},
}

@PhDThesis{Bra22,
  author      = {P. Brandner},
  date        = {2022},
  institution = {RWTH Aachen University},
  title       = {Numerical Methods for Surface Navier-Stokes Equations in Stream Function Formulation},
  doi         = {10.18154/RWTH-2022-04531},
}

@Article{AKK22,
  author       = {A. Aretaki and E. N. Karatzas and G. Katsouleas},
  date         = {2022-04},
  journaltitle = {J. Sci. Comput.},
  title        = {Equal Higher Order Analysis of an Unfitted Discontinuous Galerkin Method for Stokes Flow Systems},
  doi          = {10.1007/s10915-022-01823-w},
  number       = {2},
  volume       = {91},
  publisher    = {Springer Science and Business Media {LLC}},
}

@Article{KKT22,
  author       = {G. Katsouleas and E. N. Karatzas and F. Travlopanos},
  title        = {Discrete empirical interpolation and unfitted mesh {FEMs}: application in {PDE}-constrained optimization},
  pages        = {1--34},
  date         = {2022-02},
  doi          = {10.1080/02331934.2022.2032697},
  journaltitle = {Optimization},
  publisher    = {Informa {UK} Limited},
}

@Online{FY22,
  author      = {Fu, G. and Yang, Y.},
  title       = {A hybridizable discontinuous Galerkin method on unfitted meshes for single-phase Darcy flow in fractured porous media},
  eprint      = {2209.05445},
  eprintclass = {math.NA},
  eprinttype  = {arXiv},
  publisher   = {arXiv},
  year        = {2022-09},
}

@Online{R20,
  author      = {A. Reusken},
  date        = {2020-11-05},
  title       = {{Analysis of finite element methods for surface vector-Laplace eigenproblems}},
  eprint      = {2011.02851},
  eprintclass = {math.NA},
  eprinttype  = {arXiv},
}

@Online{OQS21,
  author      = {M. Olshanskii and A. Quaini and Q. Sun},
  date        = {2021-01-24},
  title       = {An unfitted finite element method for two-phase {Stokes} problems with slip between phases},
  eprint      = {2101.09627},
  eprintclass = {math.NA},
  eprinttype  = {arXiv},
}

@Article{vWRFH21,
  author       = {H. von Wahl and T. Richter and S. Frei and T. Hagemeier},
  date         = {2021-03-02},
  journaltitle = {Phys. Fluids},
  title        = {Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data},
  doi          = {10.1063/5.0037971},
  eid          = {033304},
  number       = {3},
  volume       = {33},
  keywords     = {physics.flu-dyn, cs.CE, cs.NA, math.NA, physics.comp-ph},
  timestamp    = {2021-01-05},
}

@Dataset{vWRFH20a,
  author    = {H. von Wahl and T. Richter and S. Frei and T. Hagemeier},
  date      = {2020-11-17},
  title     = {Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data},
  doi       = {10.5281/zenodo.3989604},
  location  = {Zenodo repository},
  timestamp = {2021-01-05},
}

@Article{vWRL20,
  author       = {H. von Wahl and T. Richter and C. Lehrenfeld},
  date         = {2021},
  journaltitle = {IMA J. Numer. Anal.},
  title        = {An unfitted {Eulerian} finite element method for the time-dependent {Stokes} problem on moving domains},
  doi          = {10.1093/imanum/drab044},
  eprint       = {2002.02352},
  eprintclass  = {math.NA},
  eprinttype   = {arXiv},
  keywords     = {math.NA, cs.NA},
  timestamp    = {2021-01-05},
}

@Dataset{vWRL20a,
  author    = {H. von Wahl and T. Richter and C. Lehrenfeld},
  date      = {2020-02-05},
  title     = {An unfitted {Eulerian} finite element method for the time-dependent {Stokes} problem on moving domains},
  doi       = {10.5281/zenodo.3647571},
  location  = {Zenodo repository},
  copyright = {GNU General Public License v3.0 only},
  keywords  = {Unfitted Finite Elements, CutFEM, Moving Domains, Flow problems},
  publisher = {Zenodo},
  timestamp = {2021-01-05},
}

@Article{BR20,
  author       = {P. Brandner and A. Reusken},
  date         = {2020-10-12},
  journaltitle = {ESAIM Math. Model. Numer. Anal.},
  title        = {Finite element error analysis of surface {Stokes} equations in stream function formulation},
  doi          = {10.1051/m2an/2020044},
  number       = {6},
  pages        = {2069--2097},
  volume       = {54},
  publisher    = {{EDP} Sciences},
  timestamp    = {2021-01-05},
}

@Article{JR19,
  author       = {T. Jankuhn and A. Reusken},
  date         = {2019-04-29},
  journaltitle = {IMA J. Numer. Anal.},
  title        = {Trace finite element methods for surface vector-Laplace equations},
  doi          = {10.1093/imanum/drz062},
  eprint       = {1904.12494},
  eprintclass  = {math.NA},
  eprinttype   = {arXiv},
  number       = {1},
  pages        = {48--83},
  volume       = {41},
  keywords     = {math.NA, 65N30, 65N12, 65N15},
  month        = may,
  publisher    = {Oxford University Press ({OUP})},
  timestamp    = {2021-01-05},
  year         = {2020},
}

@Online{JR19a,
  author      = {T. Jankuhn and A. Reusken},
  date        = {2019-09-18},
  title       = {Higher order Trace Finite Element Methods for the Surface {Stokes} Equation},
  eprint      = {1909.08327},
  eprintclass = {math.NA},
  eprinttype  = {arXiv},
  keywords    = {math.NA, cs.NA, 65N30, 65N12},
  timestamp   = {2021-01-05},
}

@Article{KBR20,
  author       = {E. N. Karatzas and F. Ballarin and G. Rozza},
  date         = {2020-02-01},
  journaltitle = {Comput. Math. with Appl.},
  title        = {Projection-based reduced order models for a cut finite element method in parametrized domains},
  doi          = {10.1016/j.camwa.2019.08.003},
  number       = {3},
  pages        = {833--851},
  volume       = {79},
  publisher    = {Elsevier {BV}},
  timestamp    = {2021-01-05},
}

@Article{LPWL16,
  author       = {P. Lederer and C.-M. Pfeiler and C. Wintersteiger and C. Lehrenfeld},
  date         = {2016-10-25},
  journaltitle = {PAMM. Proc. Appl. Math. Mech.},
  title        = {Higher order unfitted {FEM} for {Stokes} interface problems},
  doi          = {10.1002/pamm.201610003},
  number       = {1},
  pages        = {7--10},
  volume       = {16},
  publisher    = {Wiley},
  timestamp    = {2021-01-05},
}

@Article{Leh16,
  author       = {C. Lehrenfeld},
  date         = {2016-03-01},
  journaltitle = {Comput. Methods Appl. Mech. Engrg.},
  title        = {High order unfitted finite element methods on level set domains using isoparametric mappings},
  doi          = {10.1016/j.cma.2015.12.005},
  pages        = {716--733},
  volume       = {300},
  publisher    = {Elsevier {BV}},
  timestamp    = {2021-01-05},
}

@InCollection{Leh17,
  author    = {C. Lehrenfeld},
  booktitle = {Lecture Notes in Computational Science and Engineering},
  date      = {2017-03-14},
  title     = {A higher order isoparametric fictitious domain method for level set domains},
  doi       = {10.1007/978-3-319-71431-8_3},
  editor    = {S. Bordas and E. Burman and M. Larson and M. Olshanskii},
  pages     = {65--92},
  publisher = {Springer, Cham},
  volume    = {121},
  timestamp = {2021-01-05},
}

@Article{LR17,
  author       = {C. Lehrenfeld and A. Reusken},
  date         = {2017-08-18},
  journaltitle = {IMA J. Numer. Anal.},
  title        = {Analysis of a high-order unfitted finite element method for elliptic interface problems},
  doi          = {10.1093/imanum/drx041},
  number       = {3},
  pages        = {1351--1387},
  volume       = {38},
  publisher    = {Oxford University Press ({OUP})},
  timestamp    = {2021-01-05},
}

@MastersThesis{Pre18,
  author      = {J. Preu\ss},
  date        = {2018-01-31},
  institution = {Georg-August Universit\"at G\"ottingen},
  title       = {Higher order unfitted isoparametric space-time {FEM} on moving domains},
  doi         = {10.25625/UACWXS},
  timestamp   = {2021-01-05},
}

@InProceedings{HL19,
  author       = {F. Heimann and C. Lehrenfeld},
  booktitle    = {Numerical Mathematics and Advanced Applications ENUMNATH 2017},
  date         = {2019-01-05},
  title        = {Numerical integration on hyperrectangles in isoparametric unfitted finite elements},
  booksubtitle = {Lecture Notes in Computational Science and Engineering},
  doi          = {10.1007/978-3-319-96415-7_16},
  pages        = {193--202},
  publisher    = {Springer International Publishing},
  timestamp    = {2021-01-05},
}

@Article{LO19,
  author       = {C. Lehrenfeld and M. A. Olshanskii},
  date         = {2019-04-24},
  journaltitle = {ESAIM Math. Model. Numer. Anal.},
  title        = {An {Eulerian} finite element method for {PDE}s in time-dependent domains},
  doi          = {10.1051/m2an/2018068},
  number       = {2},
  pages        = {585--614},
  volume       = {53},
  publisher    = {{EDP} Sciences},
  timestamp    = {2021-01-05},
}

@Article{LR19,
  author       = {C. Lehrenfeld and A. Reusken},
  date         = {2019-12-17},
  journaltitle = {J. Numer. Math.},
  title        = {L2-error analysis of an isoparametric unfitted finite element method for elliptic interface problems},
  doi          = {10.1515/jnma-2017-0109},
  number       = {2},
  pages        = {85--99},
  volume       = {27},
  publisher    = {Walter de Gruyter {GmbH}},
  timestamp    = {2021-01-05},
}

@MastersThesis{Rau18,
  author      = {H.-G. Raumer},
  date        = {2018-03-28},
  institution = {Georg-August Universit\"at G\"ottingen},
  title       = {Shape Optimization for Interface Problems using unfitted Finite Elements},
  url         = {http://cpde.math.uni-goettingen.de/data/Rau18_Ma.pdf},
  timestamp   = {2021-01-05},
}

@Thesis{Hei18,
  author      = {F. Heimann},
  date        = {2018-09},
  institution = {Georg-August Universit\"at G\"ottingen},
  title       = {Higher order Discontinuous {Galerkin} methods for the {Laplace-Beltrami} problem on unfitted smooth surfaces},
  type        = {Bachelor's thesis},
  doi         = {10.25625/OIBRT4},
  timestamp   = {2021-01-05},
}

@PhdThesis{Lud20,
  author      = {T. Ludescher},
  date        = {2020-05-27},
  institution = {RWTH Aachen University},
  title       = {Multilevel preconditioning of stabilized unfitted finite element discretizations},
  doi         = {10.18154/RWTH-2020-07305},
  timestamp   = {2021-01-05},
}

@InProceedings{Leh16a,
  author      = {C. Lehrenfeld},
  booktitle   = {Proceedings of the {VII} European Congress on Computational Methods in Applied Sciences and Engineering ({ECCOMAS} Congress 2016)},
  date        = {2016-03-02},
  title       = {Removing the stabilization parameter in fitted and unfitted symmetric {Nitsche} formulations},
  doi         = {10.7712/100016.1820.4573},
  eprint      = {1603.00617},
  eprintclass = {math.NA},
  eprinttype  = {arXiv},
  publisher   = {Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens ({NTUA}) Greece},
  keywords    = {math.NA},
  timestamp   = {2021-01-05},
  year        = {2016},
}

@Article{GLR18,
  author       = {J. Grande and C. Lehrenfeld and A. Reusken},
  date         = {2018-01-18},
  journaltitle = {SIAM J. Numer. Anal.},
  title        = {Analysis of a High-Order Trace Finite Element Method for {PDEs} on Level Set Surfaces},
  doi          = {10.1137/16m1102203},
  number       = {1},
  pages        = {228--255},
  volume       = {56},
  publisher    = {Society for Industrial {\&} Applied Mathematics ({SIAM})},
  timestamp    = {2021-01-05},
}

@Online{AK20,
  author      = {A. Aretaki and E. N. Karatzas},
  date        = {2020-02-29},
  title       = {Random geometries for optimal control {PDE} problems based on fictitious domain {FEM}s and cut elements},
  eprint      = {2003.00352},
  eprintclass = {math.NA},
  eprinttype  = {arXiv},
  keywords    = {math.NA, cs.NA, 65C05, 65N55, 65N85, 49J20, 35Q93, 35R60},
  timestamp   = {2021-01-05},
}

@Article{LR16,
  author       = {C. Lehrenfeld and A. Reusken},
  date         = {2016-03-26},
  journaltitle = {Numer. Math.},
  title        = {Optimal preconditioners for Nitsche-{XFEM} discretizations of interface problems},
  doi          = {10.1007/s00211-016-0801-6},
  number       = {2},
  pages        = {313--332},
  volume       = {135},
  publisher    = {Springer Science and Business Media {LLC}},
  timestamp    = {2021-01-05},
}

@Online{KNBR20,
  author      = {E. N. Karatzas and M. Nonino and F. Ballarin and G. Rozza},
  date        = {2020-10-10},
  title       = {A Reduced Order Cut Finite Element method for geometrically parameterized steady and unsteady {Navier-Stokes} problems},
  eprint      = {2010.04953},
  eprintclass = {math.NA},
  eprinttype  = {arXiv},
  keywords    = {math.NA, cs.NA},
  timestamp   = {2021-01-09},
}

@MastersThesis{Hei20,
  author      = {F. Heimann},
  date        = {2020-10},
  institution = {Georg-August Universit\"at G\"ottingen},
  title       = {On Discontinuous- and Continuous-In-Time Unfitted Space-Time Methods for {PDEs} on Moving Domains},
  doi         = {10.25625/CDCMYT},
  timestamp   = {2021-01-09},
}

@Article{vWR21,
  author           = {von Wahl, H. and Richter, T.},
  date             = {2021-08-12},
  journaltitle     = {Internat. J. Numer. Methods Fluids},
  title            = {Using a deep neural network to predict the motion of under-resolved triangular rigid bodies in an incompressible flow},
  doi              = {10.1002/fld.5037},
  issue            = {12},
  pages            = {3364--2282},
  volume           = {93},
  publisher        = {Wiley},
}

@Article{fenics,
  author       = {Martin S. Aln{\ae}s and Jan Blechta and Johan Hake and August Johansson and Benjamin Kehlet and Anders Logg and Chris Richardson and Johannes Ring and Marie E. Rognes and Garth N. Wells},
  date         = {2015},
  journaltitle = {Archive of Numerical Software},
  title        = {{The FEniCS Project Version 1.5}},
  doi          = {10.11588/ans.2015.100.20553},
  number       = {100},
  volume       = {3},
  page         = {9-23},
}

@InCollection{dune:udg,
  author    = {Engwer, Christian and Heimann, Felix},
  booktitle = {Advances in DUNE},
  date      = {2012},
  title     = {{Dune-UDG}: a cut-cell framework for unfitted discontinuous {Galerkin} methods},
  doi       = {10.1007/978-3-642-28589-9_7},
  pages     = {89--100},
  publisher = {Springer},
}

@Article{dune,
  author       = {M. Blatt and A. Burchardt and A. Dedner and Ch. Engwer and J. Fahlke and B. Flemisch and Ch. Gersbacher and C. Gr\"aser and F. Gruber and Ch. Gr\"uninger and D. Kempf and R. Kl{\"o}fkorn and T. Malkmus and S. Müthing and M. Nolte and M. Piatkowski and O. Sander},
  date         = {2016},
  journaltitle = {Archive of Numerical Software},
  title        = {{The Distributed and Unified Numerics Environment, Version 2.4}},
  doi          = {10.11588/ans.2016.100.26526},
  issn         = {2197-8263},
  number       = {100},
  pages        = {13--29},
  volume       = {4},
  keywords     = {DUNE, Numerical Software},
}

@Article{dune:pdelab,
  author       = {Bastian, P. and Heimann, F. and Marnach, S.},
  date         = {2010},
  journaltitle = {Kybernetika},
  title        = {{Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE)}},
  doi          = {10338.dmlcz/140745},
  pages        = {294--315},
  volume       = {46},
}

@Article{fempar,
  author       = {Badia, Santiago and Martín, Alberto F and Principe, Javier},
  date         = {2018},
  journaltitle = {Arch. Comput. Methods Eng.},
  title        = {FEMPAR: An object-oriented parallel finite element framework},
  doi          = {10.1007/s11831-017-9244-1},
  number       = {2},
  pages        = {195--271},
  volume       = {25},
  publisher    = {Springer},
}

@Online{FX21,
  author      = {Guosheng Fu and Zhiliang Xu},
  date        = {2021-05-03},
  title       = {High-order space-time finite element methods for the Poisson-Nernst-Planck equations: Positivity and unconditional energy stability},
  eprint      = {2105.01163},
  eprintclass = {math.NA},
  eprinttype  = {arXiv},
  keywords    = {math.NA, cs.NA},
  timestamp   = {2021-05-11},
}

@Online{vWR21a,
  author       = {H. von Wahl and T. Richter},
  date         = {2021-11-10},
  title        = {Error analysis for a parabolic PDE model problem on a coupled moving domain in a fully Eulerian framework},
  creationdate = {2022-04-29T19:02:39},
  eprint       = {2111.05607},
  eprintclass  = {math.NA},
  eprinttype   = {arXiv},
  keywords     = {math.NA, cs.NA, 65M12, 65M60, 65M85},
}

@Dataset{vWR21b,
  author    = {H. von Wahl and T. Richter},
  date      = {2021},
  title     = {Error analysis for a parabolic PDE model problem on a coupled moving domain in a fully Eulerian framework - Reproduction Scripts},
  doi       = {10.5281/zenodo.6505243},
  location  = {Zenodo repository},
  copyright = {GNU General Public License v3.0 only},
  publisher = {Zenodo},
}

@PhdThesis{vWah21,
  author      = {H. M. von Wahl},
  date        = {2021-10-08},
  institution = {Otto-von-Guericke-Universität Magdeburg},
  title       = {Unfitted finite elements for fluid-rigid body interaction problems},
  doi         = {10.25673/40013},
}

@Online{OvW24,
  author           = {Olshanskii, M. and von Wahl, H.},
  date             = {2024-04-10},
  title            = {A conservative Eulerian finite element method for transport and diffusion in moving domains},
  eprint           = {2404.07130},
  eprintclass      = {math.NA},
  eprinttype       = {arXiv},
}

@Dataset{OvW24a,
  author           = {Olshanskii, M. and von Wahl, H.},
  date             = {2024-04-10},
  title            = {A conservative Eulerian finite element method for transport and diffusion in moving domains - Reproduction Scripts},
  doi              = {10.5281/zenodo.10951768},
  location         = {Zenodo repository},
}

@Comment{jabref-meta: databaseType:biblatex;}
