(untitled) (Advances in Applied Mathematics and Mechanics, 2020)
This article proposes a new P_1 nonconforming Nitsche's extended finite element method for elliptic interface problems with interface-unfitted meshes. It is shown that the stability of the discrete formulation is independent of not only the mesh size and the diffusion parameters, but also the position of the interface, showing a robustness over the location of interface. In spite of the low regularity of interface problems, the optimal convergence is obtained. Numerical experiments are carried out to validate theoretical results.