A new superconvergence for mixed finite element approximations

A new superconvergence result is established for numerical solutions of elliptic problems obtained from the mixed finite element method of Raviart-Thomas over rectangular partitions. The well-known optimal order error estimate in L-2-norm for the flux approximation is of order O(h(k+1)), where k greater than or equal to 0 is the order of polynomials employed in the Raviart-Thomas element. The new superconvergence shows an improved accuracy of order O(h(k+3)) between the mixed finite element approximation and an appropriately defined local projection of the flux variable when k > 0. A postprocessing technique using local projection methods is proposed and analyzed in order to provide a new approximate solution with the superconvergent order O(h(k+3)).