A Virtual Finite Element Method for Two Dimensional Maxwell Interface Problems with a Background Unfitted Mesh

Shuhao Cao, Long Chen, and Ruchi Guo

Mathematical Models and Methods in Applied Sciences, 2021

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 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 H(curl)-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.