Superconvergence for rectangular mixed finite elements

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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 [19] and for those of Brezzi et al. [4] we prove that the distance inL 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.