Related papers: Wavelet-based Edge Multiscale Finite Element Metho…
In this paper, we apply the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to first solving a nonlinear poroelasticity problem. The arising system consists of a nonlinear pressure equation and a…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow problems in…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
We present a multiscale mixed finite element method for solving second order elliptic equations with general $L^{\infty}$-coefficients arising from flow in highly heterogeneous porous media. Our approach is based on a multiscale spectral…
This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…
This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…
In this study, we derived a three-dimensional scaled boundary finite element formulation for heat conduction problems. By incorporating Wachspress shape functions, a polyhedral scaled boundary finite element method (PSBFEM) was proposed to…
This work is concerned with the rigorous analysis on the Generalized Multiscale Finite Element Methods (GMsFEMs) for elliptic problems with high-contrast heterogeneous coefficients. GMsFEMs are popular numerical methods for solving flow…
This paper presents a conforming thin plate bending element based on the Partition of Unity Finite Element Method (PUFEM), for the simulation of steady-state forced vibration. The issue of ensuring the continuity of displacement and slope…
We consider a singularly perturbed convection-diffusion with exponential and characteristic boundary layers. The problem is numerically solved by the FEM and SDFEM method with bilinear elements on a graded mesh. For the FEM we prove almost…
We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used to reduce the computational complexity of estimating the…
This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial…
Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion…
We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the…
In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…
We follow up on our previous work [C. Le Bris, F. Legoll and A. Lozinski, Chinese Annals of Mathematics 2013] where we have studied a multiscale finite element (MsFEM) type method in the vein of the classical Crouzeix-Raviart finite element…
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 generalized multiscale finite element method (GMsFEM) for single phase compressible flow in highly heterogeneous porous media. We follow the major steps of the GMsFEM to construct permeability dependent offline…