A nonconforming extended virtual element method for Stokes interface problems

In this paper, we propose a nonconforming extended virtual element method, which combines the extended finite element method with the nonconforming virtual element method, for solving Stokes interface problems with the unfitted-interface mesh. By introducing some stabilization terms and penalty terms, as well as some special terms defined on non-cut edges of interface elements in the discrete bilinear form, we prove the discrete inf-sup condition and obtain optimal error estimates. It is shown that all results are not only independent of the mesh size and the viscosity coefficient, but also the interface position. Numerical experiments are performed to verify theoretical results.