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Fourth‐ and Higher‐Order Finite Element Methods for the Incompressible Navier–Stokes Equations With Dirichlet Boundary Conditions
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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 Wick Advances 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 Schwering SIAM Journal on Scientific Computing 47(2) A762 (2025) https://doi.org/10.1137/24M1674182
A Gradient-Variance Weighting Physics-Informed Neural Network for Solving Integer and Fractional Partial Differential Equations
Space–time unfitted finite elements on moving explicit geometry representations
Santiago Badia, Pere A. Martorell and Francesc Verdugo Computer Methods in Applied Mechanics and Engineering 428 117091 (2024) https://doi.org/10.1016/j.cma.2024.117091
Space-time CutFEM on overlapping meshes I: simple continuous mesh motion
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 Badia Archives of Computational Methods in Engineering 30(6) 3617 (2023) https://doi.org/10.1007/s11831-023-09913-0
Error Analysis for a Parabolic PDE Model Problem on a Coupled Moving Domain in a Fully Eulerian Framework
Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems
Fabian Heimann, Christoph Lehrenfeld, Paul Stocker and Henry von Wahl ESAIM: Mathematical Modelling and Numerical Analysis 57(5) 2803 (2023) https://doi.org/10.1051/m2an/2023064
High-order unfitted characteristic finite element methods for moving interface problem of Oseen equations
A mechanically consistent model for fluid–structure interactions with contact including seepage
Erik Burman, Miguel A. Fernández, Stefan Frei and Fannie M. Gerosa Computer Methods in Applied Mechanics and Engineering 392 114637 (2022) https://doi.org/10.1016/j.cma.2022.114637
Cut finite element methods and ghost stabilization techniques for space‐time discretizations of the Navier–Stokes equations
Mathias Anselmann and Markus Bause International Journal for Numerical Methods in Fluids 94(7) 775 (2022) https://doi.org/10.1002/fld.5074
Tangential Navier–Stokes equations on evolving surfaces: Analysis and simulations
Maxim A. Olshanskii, Arnold Reusken and Alexander Zhiliakov Mathematical Models and Methods in Applied Sciences 32(14) 2817 (2022) https://doi.org/10.1142/S0218202522500658
A Fourth-Order Unfitted Characteristic Finite Element Method for Solving the Advection-Diffusion Equation on Time-Varying Domains
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 Rozza Computers & Mathematics with Applications 116 140 (2022) https://doi.org/10.1016/j.camwa.2021.07.016
Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains
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 Richter International Journal for Numerical Methods in Fluids 93(12) 3364 (2021) https://doi.org/10.1002/fld.5037
An Unfitted Finite Element Method for Two-Phase Stokes Problems with Slip Between Phases