Mixed finite element method with interface-fitted grids for the interface problems

In this paper we propose a mixed finite element method with interface-fitted grids to solve numerically the elliptic interface problem and hope that the normal continuity of the vector-functions in mixed finite element space will characterize exactly the flux jump conditions when crossing the edge between two adjacent elements. The numerical analysis and numerical experiments conducted in this paper shows that the mixed finite element method approximates the solution and the flux optimally and is a robust method to model the interface problem.