An Eulerian finite element method for PDEs in time-dependent domains
ESAIM: M2AN, 53 2 (2019) 585-614
Published online: 2019-04-24
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):
Modeling Tumor Invasion and Basement Membrane Dynamics in Colorectal Cancer: A PDE Approach
Valentin Schmid and Vincent HeuvelineProceedings in Applied Mathematics and Mechanics 26 (2) (2026)
https://doi.org/10.1002/pamm.70131
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
Unfitted Hybrid High-Order Methods Stabilized by Polynomial Extension for Elliptic Interface Problems
Erik Burman, Alexandre Ern and Romain MottierSIAM Journal on Numerical Analysis 64 (3) 601 (2026)
https://doi.org/10.1137/25M1741790
On the design of locking free ghost penalty stabilization and the relation to CutFEM with discrete extension
Erik Burman, Peter Hansbo and Mats G. LarsonNumerische Mathematik 158 (1) 249 (2026)
https://doi.org/10.1007/s00211-025-01502-6
Optimal convergence of arbitrary Lagrangian–Eulerian finite element methods for the Stokes equations in an evolving domain
Qiqi Rao, Jilu Wang and Yupei XieIMA Journal of Numerical Analysis 45 (6) 3616 (2025)
https://doi.org/10.1093/imanum/drae097
Stabilized Unfitted Finite Element Method for Poroelasticity With Weak Discontinuity
Zhijun Liu, Yuxin Tong, Yimin Zhang, Hong Zheng and Fanyu ZhangJournal of Geophysical Research: Solid Earth 130 (1) (2025)
https://doi.org/10.1029/2024JB030155
A Gradient-Variance Weighting Physics-Informed Neural Network for Solving Integer and Fractional Partial Differential Equations
Liang Zhang, Quansheng Liu, Ruigang Zhang, Liqing Yue and Zhaodong DingApplied Sciences 15 (20) 11137 (2025)
https://doi.org/10.3390/app152011137
A conforming interface approach for phase transitions in rarefied gas dynamics
Donat Weniger and Manuel TorrilhonJournal of Computational Physics 542 114376 (2025)
https://doi.org/10.1016/j.jcp.2025.114376
Exact shape derivatives with unfitted finite element methods
Jeremy T. Shahan and Shawn W. WalkerJournal of Numerical Mathematics (2025)
https://doi.org/10.1515/jnma-2024-0113
A Conservative Eulerian Finite Element Method for Transport and Diffusion in Moving Domains
Maxim Olshanskii and Henry von WahlComputational Methods in Applied Mathematics 25 (4) 961 (2025)
https://doi.org/10.1515/cmam-2024-0055
Stability of instantaneous pressures in an Eulerian finite element method for moving boundary flow problems
Maxim Olshanskii and Henry von WahlJournal of Computational Physics 533 113983 (2025)
https://doi.org/10.1016/j.jcp.2025.113983
Numerical simulations of fully Eulerian fluid-structure contact interaction using a ghost-penalty cut finite element approach
Stefan Frei, Tobias Knoke, Marc C. Steinbach, Anne-Kathrin Wenske and Thomas WickAdvances in Computational Science and Engineering 3 74 (2025)
https://doi.org/10.3934/acse.2025005
A Narrow Band Finite Element Method for the Level Set Equation
Maxim A. Olshanskii, Arnold Reusken and Paul SchweringSIAM Journal on Scientific Computing 47 (2) A762 (2025)
https://doi.org/10.1137/24M1674182
Projected gradient stabilization of sharp and diffuse interface formulations in unfitted Nitsche finite element methods
Maxim Olshanskii, Jan-Phillip Bäcker and Dmitri KuzminESAIM: Mathematical Modelling and Numerical Analysis 59 (6) 2933 (2025)
https://doi.org/10.1051/m2an/2025079
Geometry error analysis of a parametric mapping for higher order unfitted space–time methods
Fabian Heimann and Christoph LehrenfeldIMA Journal of Numerical Analysis 45 (6) 3643 (2025)
https://doi.org/10.1093/imanum/drae098
Fourth‐ and Higher‐Order Finite Element Methods for the Incompressible Navier–Stokes Equations With Dirichlet Boundary Conditions
Yang Li, Heyu Wang and Qinghai ZhangInternational Journal for Numerical Methods in Engineering 126 (17) (2025)
https://doi.org/10.1002/nme.70102
An Eulerian finite element method for the linearized Navier–Stokes problem in an evolving domain
Michael Neilan and Maxim OlshanskiiIMA Journal of Numerical Analysis 44 (6) 3234 (2024)
https://doi.org/10.1093/imanum/drad105
Space-time CutFEM on overlapping meshes I: simple continuous mesh motion
Mats G. Larson, Anders Logg and Carl LundholmNumerische Mathematik 156 (3) 1015 (2024)
https://doi.org/10.1007/s00211-024-01417-8
An Implicitly Extended Crank–Nicolson Scheme for the Heat Equation on a Time-Dependent Domain
Stefan Frei and Maneesh Kumar SinghJournal of Scientific Computing 99 (3) (2024)
https://doi.org/10.1007/s10915-024-02530-4
Space-time CutFEM on overlapping meshes II: simple discontinuous mesh evolution
Mats G. Larson and Carl LundholmNumerische Mathematik 156 (3) 1055 (2024)
https://doi.org/10.1007/s00211-024-01413-y
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
Space–time unfitted finite elements on moving explicit geometry representations
Santiago Badia, Pere A. Martorell and Francesc VerdugoComputer Methods in Applied Mechanics and Engineering 428 117091 (2024)
https://doi.org/10.1016/j.cma.2024.117091
A high-order conservative cut finite element method for problems in time-dependent domains
Sebastian Myrbäck and Sara ZahediComputer Methods in Applied Mechanics and Engineering 431 117245 (2024)
https://doi.org/10.1016/j.cma.2024.117245
Applications of a space-time FOSLS formulation for parabolic PDEs
Gregor Gantner and Rob StevensonIMA Journal of Numerical Analysis 44 (1) 58 (2024)
https://doi.org/10.1093/imanum/drad012
An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains
Fanyi Yang and Xiaoping XieAdvances in Computational Mathematics 50 (3) (2024)
https://doi.org/10.1007/s10444-024-10148-1
An integral equation method for the advection-diffusion equation on time-dependent domains in the plane
Fredrik Fryklund, Sara Pålsson and Anna-Karin TornbergJournal of Computational Physics 475 111856 (2023)
https://doi.org/10.1016/j.jcp.2022.111856
Error Analysis for a Parabolic PDE Model Problem on a Coupled Moving Domain in a Fully Eulerian Framework
Henry von Wahl and Thomas RichterSIAM Journal on Numerical Analysis 61 (1) 286 (2023)
https://doi.org/10.1137/21M1458417
Convergence Analysis of an Unfitted Mesh Semi-implicit Coupling Scheme for Incompressible Fluid-Structure Interaction
Erik Burman, Miguel A. Fernández and Fannie M. GerosaVietnam Journal of Mathematics 51 (1) 37 (2023)
https://doi.org/10.1007/s10013-022-00589-w
Geometrically Higher Order Unfitted Space-Time Methods for PDEs on Moving Domains
Fabian Heimann, Christoph Lehrenfeld and Janosch PreußSIAM Journal on Scientific Computing 45 (2) B139 (2023)
https://doi.org/10.1137/22M1476034
An Eulerian time‐stepping scheme for a coupled parabolic moving domain problem using equal‐order unfitted finite elements
Henry von Wahl and Thomas RichterPAMM 22 (1) (2023)
https://doi.org/10.1002/pamm.202200003
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
Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems
Fabian Heimann, Christoph Lehrenfeld, Paul Stocker and Henry von WahlESAIM: Mathematical Modelling and Numerical Analysis 57 (5) 2803 (2023)
https://doi.org/10.1051/m2an/2023064
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
High-order unfitted characteristic finite element methods for moving interface problem of Oseen equations
Chuwen Ma, Tian Tian and Weiying ZhengJournal of Computational and Applied Mathematics 425 115028 (2023)
https://doi.org/10.1016/j.cam.2022.115028
Space-time unfitted finite element methods for time-dependent problems on moving domains
Santiago Badia, Hridya Dilip and Francesc VerdugoComputers & Mathematics with Applications 135 60 (2023)
https://doi.org/10.1016/j.camwa.2023.01.032
A Fourth-Order Unfitted Characteristic Finite Element Method for Solving the Advection-Diffusion Equation on Time-Varying Domains
Chuwen Ma, Qinghai Zhang and Weiying ZhengSIAM Journal on Numerical Analysis 60 (4) 2203 (2022)
https://doi.org/10.1137/22M1483475
An Integral Equation Method for the Advection-Diffusion Equation on Time-Dependent Domains in the Plane
Fredrik Fryklund, Sara Pålsson and Anna-Karin TornbergSSRN Electronic Journal (2022)
https://doi.org/10.2139/ssrn.4147174
An unfitted finite element method using level set functions for extrapolation into deformable diffuse interfaces
Dmitri Kuzmin and Jan-Phillip BäckerJournal of Computational Physics 461 111218 (2022)
https://doi.org/10.1016/j.jcp.2022.111218
Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains
Erik Burman, Stefan Frei and Andre MassingNumerische Mathematik 150 (2) 423 (2022)
https://doi.org/10.1007/s00211-021-01264-x
A mechanically consistent model for fluid–structure interactions with contact including seepage
Erik Burman, Miguel A. Fernández, Stefan Frei and Fannie M. GerosaComputer Methods in Applied Mechanics and Engineering 392 114637 (2022)
https://doi.org/10.1016/j.cma.2022.114637
A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems
Efthymios N. Karatzas, Monica Nonino, Francesco Ballarin and Gianluigi RozzaComputers & Mathematics with Applications 116 140 (2022)
https://doi.org/10.1016/j.camwa.2021.07.016
Stability Analysis of Polytopic Discontinuous Galerkin Approximations of the Stokes Problem with Applications to Fluid–Structure Interaction Problems
Paola F. Antonietti, Lorenzo Mascotto, Marco Verani and Stefano ZoncaJournal of Scientific Computing 90 (1) (2022)
https://doi.org/10.1007/s10915-021-01695-6
Isoparametric Unfitted BDF--Finite Element Method for PDEs on Evolving Domains
Yimin Lou and Christoph LehrenfeldSIAM Journal on Numerical Analysis 60 (4) 2069 (2022)
https://doi.org/10.1137/21M142126X
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
Cut finite element methods and ghost stabilization techniques for space‐time discretizations of the Navier–Stokes equations
Mathias Anselmann and Markus BauseInternational Journal for Numerical Methods in Fluids 94 (7) 775 (2022)
https://doi.org/10.1002/fld.5074
A fourth-order unfitted characteristic finite element method for free-boundary problems
Chuwen Ma and Weiying ZhengJournal of Computational Physics 469 111552 (2022)
https://doi.org/10.1016/j.jcp.2022.111552
An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains
Henry von Wahl, Thomas Richter and Christoph LehrenfeldIMA Journal of Numerical Analysis 42 (3) 2505 (2022)
https://doi.org/10.1093/imanum/drab044
An Unfitted Finite Element Method for Two-Phase Stokes Problems with Slip Between Phases
Maxim Olshanskii, Annalisa Quaini and Qi SunJournal of Scientific Computing 89 (2) (2021)
https://doi.org/10.1007/s10915-021-01658-x
Two-point block variable order step size multistep method for solving higher order ordinary differential equations directly
Ahmad Fadly Nurullah Rasedee, Mohammad Hasan Abdul Sathar, Siti Raihana Hamzah, et al.Journal of King Saud University - Science 33 (3) 101376 (2021)
https://doi.org/10.1016/j.jksus.2021.101376
Using a deep neural network to predict the motion of underresolved triangular rigid bodies in an incompressible flow
Henry von Wahl and Thomas RichterInternational Journal for Numerical Methods in Fluids 93 (12) 3364 (2021)
https://doi.org/10.1002/fld.5037
Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data
Henry von Wahl, Thomas Richter, Stefan Frei and Thomas HagemeierPhysics of Fluids 33 (3) (2021)
https://doi.org/10.1063/5.0037971
A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains
C M Elliott and T RannerIMA Journal of Numerical Analysis 41 (3) 1696 (2021)
https://doi.org/10.1093/imanum/draa062
A finite element method for Allen–Cahn equation on deforming surface
Maxim Olshanskii, Xianmin Xu and Vladimir YushutinComputers & Mathematics with Applications 90 148 (2021)
https://doi.org/10.1016/j.camwa.2021.03.018
A higher order fictitious domain method for the Navier–Stokes equations
Markus Bause and Mathias AnselmannPAMM 20 (1) (2021)
https://doi.org/10.1002/pamm.202000038
A weighted Shifted Boundary Method for free surface flow problems
Oriol Colomés, Alex Main, Léo Nouveau and Guglielmo ScovazziJournal of Computational Physics 424 109837 (2021)
https://doi.org/10.1016/j.jcp.2020.109837
Solution of Reynolds lubrication equation on evolving surfaces
Elizaveta Vyacheslavovna Zipunova, Anton Valerievich Ivanov and Evgeny Borisovich SavenkovKeldysh Institute Preprints (13) 1 (2020)
https://doi.org/10.20948/prepr-2020-13
Mass conservative reduced order modeling of a free boundary osmotic cell swelling problem
Christoph Lehrenfeld and Stephan RaveAdvances in Computational Mathematics 45 (5-6) 2215 (2019)
https://doi.org/10.1007/s10444-019-09691-z
Preconditioning immersed isogeometric finite element methods with application to flow problems
F. de Prenter, C.V. Verhoosel and E.H. van BrummelenComputer Methods in Applied Mechanics and Engineering 348 604 (2019)
https://doi.org/10.1016/j.cma.2019.01.030