A nonconforming immersed virtual element method for elliptic interface problems

Abstract

This paper presents the lowest-order nonconforming immersed virtual element method for solving elliptic interface problems on unfitted polygonal meshes. The local discrete space on each interface mesh element consists of the solutions of local interface problems with Neumann boundary conditions, and the elliptic projection is modified so that its range is the space of broken linear polynomials satisfying the interface conditions. We derive optimal error estimates in the broken H1-norm and L2-norm, under the piecewise H2-regulartiy assumption. In our scheme, the mesh assumptions for error analysis allow small cut elements. Several numerical experiments are provided to confirm the theoretical results.