An immersed finite element method for orthotropic interface problem

In this paper we develop an immersed interface finite element(IFE) method based on rectangular mesh for a kind of anisotropy diffusion models which is governed by an elliptic interface problem with discontinuous tensor-coefficients. The method is based on bilinear polynomials on non-interface rectangular elements and piecewise bilinear polynomials on interface rectangular elements. We prove that a function of the IFE space is uniquely determined by the values of vertices on the elements. Then, we construct the IFE space, define an IFE formulation and prove that the IFE formulation is uniquely solvable. At last, we obtain the optimal order H¹ and L² convergence results for the IFE solution, which are O(h) and O(h²) respectively.