A Nonconforming Extended Virtual Element Method for Elliptic Interface Problems

This paper proposes a nonconforming extended virtual element method for solving elliptic interface problems with interface-unfitted meshes. The discrete approximation form is presented by adding some special terms along the edges of interface elements and several stabilization terms in the discrete bilinear form. The well-posedness of the discrete scheme is obtained and the optimal convergence is proven under the energy norm. It is shown that all results are independent of the position of the interface relative to the mesh and the contrast between the diffusion coefficients. Furthermore, short edges are allowed to appear in the mesh by modifying the stabilization term of the nonconforming virtual element method. Some numerical experiments are performed to verify the theoretical results.