(untitled) (Journal of Computational Mathematics, 2018)
In this paper, we present a weak Galerkin (WG) mixed finite element method for solving the second-order elliptic equations with Robin boundary conditions. Stability and a priori error estimates for the coupled method are derived. We present the optimal order error estimate for the WG-MFEM approximations in a norm that is related to the L^2 for the flux and H^1 for the scalar function. Also an optimal order error estimate in L^2 is derived for the scalar approximation by using a duality argument. A series of numerical experiments is presented that verify our theoretical results.