  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.
