Summary.
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 \(H(\mbox{div;} \Omega)\)-distance between the approximate solution and a suitable projection of the real solution is of higher order than the \(H(\mbox{div;} \Omega)\)-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\(L^2(\Omega)\) -error in the approximation of the vector variable.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received December 6, 1992 / Revised version received October 2, 1993
Rights and permissions
About this article
Cite this article
Brandts, J. Superconvergence and a posteriori error estimation for triangular mixed finite elements . Numer. Math. 68, 311–324 (1994). https://doi.org/10.1007/s002110050064
Issue Date:
DOI: https://doi.org/10.1007/s002110050064