Optimal Quadratic Nitsche Extended Finite Element Method for Interface Problem of Diffusion Equation (Journal of Computational Mathematics, 2018)
In this paper, we study Nitsche extended finite element method (XFEM) for the interfaceproblem of a two dimensional diffusion equation. Specifically, we study the quadraticXFEM scheme on some shape-regular family of grids and prove the optimal convergencerate of the scheme with respect to the mesh size. Main efforts are devoted onto classifyingthe cases of intersection between the elements and the interface and prove a weighted traceinequality for the extended finite element functions needed, and the general framework ofanalysing XFEM can be implemented then.