A virtual finite element method for two-dimensional Maxwell interface problems with a background unfitted mesh

Author:

Cao Shuhao1,Chen Long2,Guo Ruchi2

Affiliation:

1. Department of Mathematics and Statistics, Washington University in St. Louis, St. Louis, MO 63130, USA

2. Department of Mathematics, University of California Irvine, Irvine, CA 92697, USA

Abstract

A virtual element method (VEM) with the first-order optimal convergence order is developed for solving two-dimensional Maxwell interface problems on a special class of polygonal meshes that are cut by the interface from a background unfitted mesh. A novel virtual space is introduced on a virtual triangulation of the polygonal mesh satisfying a maximum angle condition, which shares exactly the same degrees of freedom as the usual [Formula: see text]-conforming virtual space. This new virtual space serves as the key to prove that the optimal error bounds of the VEM are independent of high aspect ratio of the possible anisotropic polygonal mesh near the interface.

Funder

National Science Foundation

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation

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