A posteriori error estimator for a mixed finite element method for Reissner-Mindlin plate

Abstract

We present an a posteriori error estimator for a mixed finite element method for the Reissner-Mindlin plate model. The finite element method we deal with, was analyzed by Durán and Liberman in 1992 and can also be seen as a particular example of the general family analyzed by Brezzi, Fortin, and Stenberg in 1991. The estimator is based on the evaluation of the residual of the finite element solution. We show that the estimator yields local lower and global upper bounds of the error in the numerical solution in a natural norm for the problem, which includes the H1 norms of the terms corresponding to the deflection and the rotation and a dual norm for the shearing force. The estimates are valid uniformly with respect to the plate thickness.