Author: Rolf Stenberg
Title of the contribution: Mixed finite element methods, superconvergence, postprocessing and a-posteriori estimates
Abstract:
We consider mixed finite element methods for two problems, the Poisson equation and the equations for Reissner-Mindlin plates. For the Poisson problem it was discovered by Arnold and Brezzi that even if the mixed method is designed in order to get a good approximation for the flux variable, i.e. the gradient of the displacement, the solution has some interesting superconvergence properties that can be utilized in postprocessing in order to get an improved approximation for the displacement. In our work we show that the postprocessed displacement can be used in order to get an efficient a posteriori error bound for the solution. Next, we show the analog for the Reissner-Mindlin equations approximated by a linked mixed method. The solution of the linked method is in a sense superconvergent and this gives a new way of designing a posteriori estimates.
This is joint work with Carlo Lovadina, Pavia, cf.
C. Lovadina, R. Stenberg. A posteriori error analysis of the linked interpolation technique for plate bending problems. SIAM Journal of Numerical Analysis, accepted for publication.
C. Lovadina, R. Stenberg. Energy norm a posteriori error estimates for mixed finite element methods. Mathematics of Computation, accepted for publication.
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