A NOTE ON UNIFORM SUPERCONVERGENCE FOR THE TIMOSHENKO BEAM USING MIXED FINITE ELEMENTS

Abstract

In this paper we present some results on the discretization by mixed finite elements of the Timoshenko beam, i.e. the one-dimensional Reissner-Mindlin plate bending problem. The results concern superconvergence. Superconvergence (of the displacement at nodal points and of the gradient at Gaussian points) for plate bending problems was considered before, but these earlier results degenerate for small values of the plate thickness d. Here, we prove superconvergence of the mixed finite element solutions to projections of the real solutions on the approximating spaces in the global H1(I)-norm uniform in d. These facts can be used to obtain asymptotically exact a posteriori error estimators, uniform in d, by means of an easy implementable and cheap post-processing. Numerical experiments illustrate the conclusions.