SUPERCONVERGENCE AND A-POSTERIORI ERROR ESTIMATION FOR TRIANGULAR MIXED FINITE-ELEMENTS

In this paper, we prove superconvergence results for the vector variable when lowest order triangular mixed finite elements of Raviart-Thomas type [17] on uniform triangulations are used, i.e., that the H(div;OMEGA)-distance between the approximate solution and a suitable projection of the real solution is of higher order than the H(div;OMEGA)-error. We prove results for both Dirichlet and Neumann boundary conditions. Recently, Duran [9] proved similar results for rectangular mixed finite elements, and superconvergence along the Gauss-lines for rectangular mixed finite elements was considered by Douglas, Ewing, Lazarov and Wang in [11], [8], and [18]. The triangular case however needs some extra effort. Using the superconvergence results, a simple postprocessing of the approximate solution will give an asymptotically exact a posteriori error estimator for the L2(OMEGA)-error in the approximation of the vector variable.