A Nonconforming Virtual Element Method for the Elliptic Interface Problem

In this paper, we propose a nonconforming virtual element method for the elliptic interface problem based on an unfitted polygonal mesh.On interface elements, the intersecting points of the interface and the edges of elements are considered as additional nodes of the mesh, and then we present a virtual element space satisfying the interface conditions.On non-interface elements, we use the usual nonconforming virtual element.By employing a computable operator, we introduce a discrete scheme and obtain optimal convergence results which are independent of the contrast of the coefficients.Numerical examples are presented to validate the theoretical results.