Related papers: Constraint energy minimizing generalized multiscal…
In this work, we analyze a penalized variant of the {\phi}-FEM scheme for the Poisson equation with Dirichlet boundary conditions. The {\phi}-FEM is a recently introduced unfitted finite element method based on a level-set description of…
In this paper, we study arbitrary order extended finite element (XFE) methods based on two discontinuous Galerkin (DG) schemes in order to solve elliptic interface problems in two and three dimensions. Optimal error estimates in the…
We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…
Invariance-principle-based methods such as Invariant Risk Minimization (IRM), have recently emerged as promising approaches for Domain Generalization (DG). Despite promising theory, such approaches fail in common classification tasks due to…
We generalize the closest point method (CPM) to solve surface partial differential equations with general boundary conditions. The proposed extrapolation method provides a unified framework for treating a broad class of inhomogeneous…
We show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type where we consider the case when the exact solution $u \in H^s$…
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…
We present a multiscale finite element method for a diffusion problem with rough and high contrast coefficients. The construction of the multiscale finite element space is based on the localized orthogonal decomposition methodology and it…
This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including Dirichlet, Neumann, and Robin conditions. We examine MIM…
This paper focusses on the optimal control problems governed by fourth-order linear elliptic equations with clamped boundary conditions in the framework of the Hessian discretisation method (HDM). The HDM is an abstract framework that…
We propose an unfitted interface penalty Discontinuous Galerkin-Finite Element Method (UIPDG-FEM) for elliptic interface problems. This hybrid method combines the interior penalty discontinuous Galerkin (IPDG) terms near the…
A hybrid computational approach that integrates the finite element method (FEM) with least squares support vector regression (LSSVR) is introduced to solve partial differential equations. The method combines FEM's ability to provide the…
In this paper, we propose a coupled Discrete Empirical Interpolation Method (DEIM) and Generalized Multiscale Finite element method (GMsFEM) to solve nonlinear parabolic equations with application to the Allen-Cahn equation. The Allen-Cahn…
This work establishes the well-posedness and a priori error analysis for the mixed FEEC-type finite element approximation of the three-dimensional vector Laplace boundary value problem subject to the Dirichlet boundary condition. The…
In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…
In this paper, we study the numerical method for the bi-Laplace problems with inhomogeneous coefficients; particularly, we propose finite element schemes on rectangular grids respectively for an inhomogeneous fourth-order elliptic singular…
In recent work, Li et al.\ (Comm.\ Math.\ Sci., 7:81-107, 2009) developed a diffuse-domain method (DDM) for solving partial differential equations in complex, dynamic geometries with Dirichlet, Neumann, and Robin boundary conditions. The…
A handy technique for the Finite Element Method (FEM) is presented that uses the null space for the implementation of Dirichlet and constraint boundary conditions. The focus of this method is to present an illustrative approach to modeling…
We introduce a new multimesh finite element method for direct numerical simulation of incompressible particulate flows. The proposed approach falls into the category of overlapping domain decomposition / Chimera / overset grid meshes. In…
Moment based methods have produced efficient multiscale quantization algorithms for solving singular perturbation/strong coupling problems. One of these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev. Lett.{\bf…