A posteriori error estimates of hp spectral element methods for integral state constrained elliptic optimal control problems

摘要

In this paper, we investigate the hp spectral element approximation for optimal control problem governed by elliptic equation with an integral constraint for state. We first present the optimality conditions of the continuous and discretized control problems, respectively. Then, hp a posteriori error estimates are obtained for the coupled state and control approximation. In the end, we use a simple and yet efficient projection algorithm to carry out ample numerical experiments which confirm our analytical results. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.