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 in [16] and can also be seen as a particular example of the general family analyzed in [13]. The estimator is based on the evaluation of the residual of the finite element solution. We show that the estimator yields locally lower and globally upper bounds of the error in the numerical solution in a natural norm for the problem, which includes the H} 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.