This paper studies the combination of the mixed covolume method with the expanded mixed element method for elliptic problems defined on a rectangle
. The lowest order Raviart-Thomas element on a rectangular grid is used. The analytical results include the uniqueness of the discrete solution if the mesh is sufficiently fine, the first order convergence in
and superconvergence results for discrete norms. Second order superconvergence can be achieved if the grid becomes sufficiently fine near the boundary. The method can be transformed into a scalar finite difference scheme for one of the variables if an appropriate quadrature rule is used. Simple numerical examples support the analytical results.