相关论文: Partially Explicit Generalized Multiscale Method f…

We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed…

We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…

In this paper, a generalized finite element method (GFEM) with optimal local approximation spaces for solving high-frequency heterogeneous Helmholtz problems is systematically studied. The local spaces are built from selected eigenvectors…

This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on…

This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…

We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled. This setting includes poroelasticity, thermoelasticity, as…

We propose a parametric finite element method (PFEM) for efficiently solving the morphological evolution of solid-state dewetting of thin films on a flat rigid substrate in three dimensions (3D). The interface evolution of the dewetting…

This paper focuses on the study of the Filament Based Lamellipodium Model (FBLM) and the corresponding Finite Element Method (FEM) from a numerical point of view. We study fundamental numerical properties of the FEM and justify the further…

In this paper, we consider a time-dependent discrete network model with highly varying connectivity. The approximation by time is performed using an implicit scheme. We propose the coarse scale approximation construction of network models…

In this work, we develop a localized numerical scheme with low regularity requirements for solving time-fractional integro-differential equations. First, a fully discrete numerical scheme is constructed. Specifically, for temporal…

Numerical treatment of the problem of two-dimensional viscous fluid flow in and around circular porous inclusions is considered. The mathematical model is described by Navier-Stokes equation in the free flow domain $\Omega_f$ and nonlinear…

We propose a stochastic multiscale finite element method (StoMsFEM) to solve random elliptic partial differential equations with a high stochastic dimension. The key idea is to simultaneously upscale the stochastic solutions in the physical…

We present an implicit-explicit (IMEX) scheme for semilinear wave equations with strong damping. By treating the nonlinear, nonstiff term explicitly and the linear, stiff part implicitly, we obtain a method which is not only unconditionally…

A modeling of metasurfaces in the finite element method (FEM) based on generalized sheet transition conditions (GSTCs) is presented. The discontinuities in electromagnetic fields across a metasurface as represented by the GSTC are modeled…

We present a cut finite element method for the heat equation on two overlapping meshes: a stationary background mesh and an overlapping mesh that moves around inside/"on top" of it. Here the overlapping mesh is prescribed a simple…

The Generalized Finite Element Method (GFEM) is a Partition of Unity Method (PUM), where the trial space of standard Finite Element Method (FEM) is augmented with non-polynomial shape functions with compact support. These shape functions,…

In this thesis we develop a stabilised finite element method for solving the equations of poroelasticity to enable solving complex models of biological tissues such as the human lungs. For the proposed numerical scheme, we use the lowest…

Modeling contact mechanics with high contrast coefficients presents significant mathematical and computational challenges, especially in achieving strongly symmetric stress approximations for mixed formulations. Due to the inherent…

The goal of this paper is to develop and analyze some fully discrete finite element methods for a displacement-pressure model modeling swelling dynamics of polymer gels under mechanical constraints. In the model, the swelling dynamics is…

We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted piecewise…