Cut finite element methods for partial differential equations on embedded manifolds of arbitrary codimensions
ESAIM: M2AN, 52 6 (2018) 2247-2282
Published online: 2019-02-01
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
An Immersed Finite Element Method for Anisotropic Elliptic Interface Problems with Nonhomogeneous Jump Conditions
Haifeng Ji and Zhilin LiJournal of Scientific Computing 106 (1) (2026)
https://doi.org/10.1007/s10915-025-03155-x
Unfitted finite element modelling of surface-bulk viscous flows in animal cells
Eric Neiva and Hervé TurlierJournal of Computational Physics 560 114926 (2026)
https://doi.org/10.1016/j.jcp.2026.114926
Analysis of a space-time unfitted finite element method for PDEs on evolving surfaces
Arnold Reusken and Hauke SassJournal of Numerical Mathematics (2026)
https://doi.org/10.1515/jnma-2024-0002
Simultaneous solution of incompressible Navier–Stokes flows on multiple surfaces
Michael Wolfgang Kaiser and Thomas-Peter FriesArchive of Applied Mechanics 95 (10) (2025)
https://doi.org/10.1007/s00419-025-02935-z
Improved Numerical Robustness of the X‐FFT Solver via Internal Scaling
Flavia Gehrig and Matti SchneiderPAMM 25 (4) (2025)
https://doi.org/10.1002/pamm.70042
153 425 (2025)
https://doi.org/10.1007/978-3-031-86173-4_43
The use of polynomial-augmented RBF collocation method with ghost points for plane elastostatic equations of anisotropic functionally graded materials
Ömer OruçComputers & Mathematics with Applications 184 116 (2025)
https://doi.org/10.1016/j.camwa.2025.02.019
Analysis of divergence-preserving unfitted finite element methods for the mixed Poisson problem
Christoph Lehrenfeld, Tim van Beeck and Igor VoulisMathematics of Computation 94 (354) 1667 (2024)
https://doi.org/10.1090/mcom/4027
Transient-pressure modelling in fractured porous media with a new embedded finite element approach
Behnam V. Damirchi, Pouria Behnoudfar, Luís A.G. Bitencourt, Osvaldo L. Manzoli and Daniel Dias-da-CostaAdvances in Water Resources 190 104730 (2024)
https://doi.org/10.1016/j.advwatres.2024.104730
An adaptive stabilized trace finite element method for surface PDEs
Timo Heister, Maxim A. Olshanskii and Vladimir YushutinComputers & Mathematics with Applications 171 164 (2024)
https://doi.org/10.1016/j.camwa.2024.07.016
Simultaneous analysis of continuously embedded Reissner–Mindlin shells in 3D bulk domains
Michael Wolfgang Kaiser and Thomas‐Peter FriesInternational Journal for Numerical Methods in Engineering 125 (16) (2024)
https://doi.org/10.1002/nme.7495
A Numerical Method for Solving Elliptic Equations on Real Closed Algebraic Curves and Surfaces
Wenrui Hao, Jonathan D. Hauenstein, Margaret H. Regan and Tingting TangJournal of Scientific Computing 99 (2) (2024)
https://doi.org/10.1007/s10915-024-02516-2
Cut Finite Element Discretizations of Cell-by-Cell EMI Electrophysiology Models
Nanna Berre, Marie E. Rognes and André MassingSIAM Journal on Scientific Computing 46 (4) B527 (2024)
https://doi.org/10.1137/23M1580632
Analysis of optimal preconditioners for CutFEM
Sven Gross and Arnold ReuskenNumerical Linear Algebra with Applications 30 (5) (2023)
https://doi.org/10.1002/nla.2486
Stabilized cut discontinuous Galerkin methods for advection–reaction problems on surfaces
Tale Bakken Ulfsby, André Massing and Simon StickoComputer Methods in Applied Mechanics and Engineering 413 116109 (2023)
https://doi.org/10.1016/j.cma.2023.116109
Tangential errors of tensor surface finite elements
Hanne Hardering and Simon PraetoriusIMA Journal of Numerical Analysis 43 (3) 1543 (2023)
https://doi.org/10.1093/imanum/drac015
An Eulerian finite element method for tangential Navier-Stokes equations on evolving surfaces
Maxim Olshanskii, Arnold Reusken and Paul SchweringMathematics of Computation 93 (349) 2031 (2023)
https://doi.org/10.1090/mcom/3931
Diffusion of tangential tensor fields: numerical issues and influence of geometric properties
E. Bachini, P. Brandner, T. Jankuhn, M. Nestler, S. Praetorius, A. Reusken and A. VoigtJournal of Numerical Mathematics (2023)
https://doi.org/10.1515/jnma-2022-0088
On the simultaneous solution of structural membranes on all level sets within a bulk domain
Thomas-Peter Fries and Michael Wolfgang KaiserComputer Methods in Applied Mechanics and Engineering 415 116223 (2023)
https://doi.org/10.1016/j.cma.2023.116223
Hybridized isogeometric method for elliptic problems on CAD surfaces with gaps
Tobias Jonsson, Mats G. Larson and Karl LarssonComputer Methods in Applied Mechanics and Engineering 410 116014 (2023)
https://doi.org/10.1016/j.cma.2023.116014
Rigorous code verification for non-linear Kirchhoff–Love shells based on tangential differential calculus with application to Isogeometric Analysis
M.H. GfrererFinite Elements in Analysis and Design 227 104041 (2023)
https://doi.org/10.1016/j.finel.2023.104041
Stability and Conditioning of Immersed Finite Element Methods: Analysis and Remedies
Frits de Prenter, Clemens V. Verhoosel, E. Harald van Brummelen, Mats G. Larson and Santiago BadiaArchives of Computational Methods in Engineering 30 (6) 3617 (2023)
https://doi.org/10.1007/s11831-023-09913-0
An accurate and robust Eulerian finite element method for partial differential equations on evolving surfaces
Hauke Sass and Arnold ReuskenComputers & Mathematics with Applications 146 253 (2023)
https://doi.org/10.1016/j.camwa.2023.06.040
Recycling augmented Lagrangian preconditioner in an incompressible fluid solver
Maxim A. Olshanskii and Alexander ZhiliakovNumerical Linear Algebra with Applications 29 (2) (2022)
https://doi.org/10.1002/nla.2415
Finite Element Discretization Methods for Velocity-Pressure and Stream Function Formulations of Surface Stokes Equations
Philip Brandner, Thomas Jankuhn, Simon Praetorius, Arnold Reusken and Axel VoigtSIAM Journal on Scientific Computing 44 (4) A1807 (2022)
https://doi.org/10.1137/21M1403126
Equal Higher Order Analysis of an Unfitted Discontinuous Galerkin Method for Stokes Flow Systems
Aikaterini Aretaki, Efthymios N. Karatzas and Georgios KatsouleasJournal of Scientific Computing 91 (2) (2022)
https://doi.org/10.1007/s10915-022-01823-w
Tangential Navier–Stokes equations on evolving surfaces: Analysis and simulations
Maxim A. Olshanskii, Arnold Reusken and Alexander ZhiliakovMathematical Models and Methods in Applied Sciences 32 (14) 2817 (2022)
https://doi.org/10.1142/S0218202522500658
A cut finite-element method for fracture and contact problems in large-deformation solid mechanics
Michael Poluektov and Łukasz FigielComputer Methods in Applied Mechanics and Engineering 388 114234 (2022)
https://doi.org/10.1016/j.cma.2021.114234
An Unfitted dG Scheme for Coupled Bulk-Surface PDEs on Complex Geometries
Christian Engwer and Sebastian WesterheideComputational Methods in Applied Mathematics 21 (3) 569 (2021)
https://doi.org/10.1515/cmam-2020-0056
A $$C^1$$-continuous Trace-Finite-Cell-Method for linear thin shell analysis on implicitly defined surfaces
Michael H. GfrererComputational Mechanics 67 (2) 679 (2021)
https://doi.org/10.1007/s00466-020-01956-5
Error analysis of higher order Trace Finite Element Methods for the surface Stokes equation
Thomas Jankuhn, Maxim A. Olshanskii, Arnold Reusken and Alexander ZhiliakovJournal of Numerical Mathematics 29 (3) 245 (2021)
https://doi.org/10.1515/jnma-2020-0017
Inf-sup stability of the trace 𝐏₂–𝐏₁ Taylor–Hood elements for surface PDEs
Maxim Olshanskii, Arnold Reusken and Alexander ZhiliakovMathematics of Computation 90 (330) 1527 (2021)
https://doi.org/10.1090/mcom/3551
An unfitted finite element method for the Darcy problem in a fracture network
Alexey Y. Chernyshenko and Maxim A. OlshanskiiJournal of Computational and Applied Mathematics 366 112424 (2020)
https://doi.org/10.1016/j.cam.2019.112424
Finite element error analysis of surface Stokes equations in stream function formulation
Philip Brandner and Arnold ReuskenESAIM: Mathematical Modelling and Numerical Analysis 54 (6) 2069 (2020)
https://doi.org/10.1051/m2an/2020044
A stabilized cut streamline diffusion finite element method for convection–diffusion problems on surfaces
Erik Burman, Peter Hansbo, Mats G. Larson, André Massing and Sara ZahediComputer Methods in Applied Mechanics and Engineering 358 112645 (2020)
https://doi.org/10.1016/j.cma.2019.112645
A mixed-dimensional CutFEM methodology for the simulation of fibre-reinforced composites
P. Kerfriden, S. Claus and I. MihaiAdvanced Modeling and Simulation in Engineering Sciences 7 (1) (2020)
https://doi.org/10.1186/s40323-020-00154-5
A higher‐order Trace finite element method for shells
Daniel Schöllhammer and Thomas‐Peter FriesInternational Journal for Numerical Methods in Engineering (2020)
https://doi.org/10.1002/nme.6558
Numerical modeling of phase separation on dynamic surfaces
Vladimir Yushutin, Annalisa Quaini and Maxim OlshanskiiJournal of Computational Physics 407 109126 (2020)
https://doi.org/10.1016/j.jcp.2019.109126
12143 32 (2020)
https://doi.org/10.1007/978-3-030-50436-6_3
Hybridized CutFEM for Elliptic Interface Problems
Erik Burman, Daniel Elfverson, Peter Hansbo, Mats G. Larson and Karl LarssonSIAM Journal on Scientific Computing 41 (5) A3354 (2019)
https://doi.org/10.1137/18M1223836
Numerical Geometry, Grid Generation and Scientific Computing
Jakob W. Stanford and Thomas-Peter FriesLecture Notes in Computational Science and Engineering, Numerical Geometry, Grid Generation and Scientific Computing 131 193 (2019)
https://doi.org/10.1007/978-3-030-23436-2_14
Interface-Capturing Method for Free-Surface Plunging and Breaking Waves
Lixing Zhu, Shoaib A. Goraya and Arif MasudJournal of Engineering Mechanics 145 (11) (2019)
https://doi.org/10.1061/(ASCE)EM.1943-7889.0001641
Higher-Order Accurate Meshing of Nonsmooth Implicitly Defined Surfaces and Intersection Curves
J. W. Stanford and T. P. FriesComputational Mathematics and Mathematical Physics 59 (12) 2093 (2019)
https://doi.org/10.1134/S0965542519120169
Monolithic cut finite element–based approaches for fluid‐structure interaction
Benedikt Schott, Christoph Ager and Wolfgang A. WallInternational Journal for Numerical Methods in Engineering 119 (8) 757 (2019)
https://doi.org/10.1002/nme.6072
A Penalty Finite Element Method for a Fluid System Posed on Embedded Surface
Maxim A. Olshanskii and Vladimir YushutinJournal of Mathematical Fluid Mechanics 21 (1) (2019)
https://doi.org/10.1007/s00021-019-0420-y
Cut finite elements for convection in fractured domains
Erik Burman, Peter Hansbo, Mats G. Larson and Karl LarssonComputers & Fluids 179 726 (2019)
https://doi.org/10.1016/j.compfluid.2018.07.022