  For elliptic interface problems in two- and three-dimensions with a possible
very low regularity, this paper establishes a priori error estimates for the
Raviart-Thomas and Brezzi-Douglas-Marini mixed finite element approximations.
These estimates are robust with respect to the diffusion coefficient and
optimal with respect to the local regularity of the solution. Several versions
of the robust best approximations of the flux and the potential approximations
are obtained. These robust and local optimal a priori estimates provide
guidance for constructing robust a posteriori error estimates and adaptive
methods for the mixed approximations.
