Superconvergence and a Posteriori Error Estimation for Triangular Mixed Nite Elements

In this paper,we prove superconvergence results for the vector variable when lowest order triangular mixed nite elements of Raviart-Thomas type 17] on uniform triangulations are used, i.e., that the H(div;)-distance between the approximate solution and a suitable projection of the real solution is of higher order than the H(div;)-error. We prove results for both Dirichlet and Neumann boundary conditions. Recently, Duran 9] proved similar results for rectangular mixed nite elements, and superconvergence along the Gauss-lines for rectangular mixed nite elements was considered by Douglas, Ewing, Lazarov and Wang in 11], 8] and 18]. The triangular case however needs some extra eeort. Using the superconvergence results, a simple postprocessing of the approximate solution will give an asymptotically exact a posteriori error estimator for the L 2 ()-error in the approximation of the vector variable.