Superconvergence for rectangular mixed finite elements (Q582829)

This paper deals with superconvergence for the vector variable in mixed finite element approximations of second order elliptic problems. For the rectangular elements of Raviart and Thomas and for those of Brezzi, Douglas, Fortin and Marini, it is proven that the distance in \(L^ 2\) between the approximate solution and a suitable interpolation 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 simple local post processing.