Superconvergence of H1-Galerkin mixed finite element methods for parabolic problems

In this article, we study the semidiscrete H1-Galerkin mixed finite element method for parabolic problems over rectangular partitions. The well-known optimal order error estimate in the L2-norm for the flux is of order O(hk+1) (SIAM J. Numer. Anal. 35 (2), (1998), pp. 712-727), where k epsilon 1 is the order of the approximating polynomials employed in the Raviart-Thomas element. We derive a superconvergence estimate of order O(hk+3) between the H1-Galerkin mixed finite element approximation and an appropriately defined local projection of the flux variable when k epsilon 1. A the new approximate solution for the flux with superconvergence of order O(hk+3) is realized via a postprocessing technique using local projection methods.