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A virtual element method (VEM) with the first order optimal convergence orderis developed for solving two-dimensional Maxwell interface problems on aspecial class of polygonal meshes that are cut by the interface from abackground unfitted mesh. A novel virtual space is introduced on a virtualtriangulation of the polygonal mesh satisfying a maximum angle condition, whichshares exactly the same degrees of freedom as the usual H(curl)-conformingvirtual space. This new virtual space serves as the key to prove that theoptimal error bounds of the VEM are independent of high aspect ratio of thepossible anisotropic polygonal mesh near the interface.

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