An extended mixed finite element method for elliptic interface problems

Abstract: In this paper, we propose an extended mixed finite element method for elliptic interface problems. By adding some stabilization terms, we present a mixed approximation form based on Brezzi-Douglas-Marini element space and the piecewise constant function space, and show that the discrete inf-sup constant is independent of how the interface intersects the triangulation. Furthermore, we derive that the optimal convergence holds independent of the location of the interface relative to the mesh. Finally, some numerical examples are presented to verify our theoretical results.