Superconvergence for rectangular mixed finite elements

Abstract

In this paper we prove superconvergence error estimates for the vector variable for mixed finite element approximations of second order elliptic problems. For the rectangular finite elements of Raviart and Thomas and for those of Brezzi et al. we prove that the distance in L 2 between the approximate solution and a projection of the exact one is of higher order than the error itself. This result is exploited to obtain superconvergence at Gaussian points and to construct higher order approximations by a local postprocessing.