TY - JOUR T1 - A Posteriori Error Estimates for $hp$ Spectral Element Approximation of Elliptic Control Problems with Integral Control and State Constraints AU - Zhang , Jinling AU - Chen , Yanping AU - Huang , Yunqing AU - Huang , Fenglin JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 469 EP - 493 PY - 2022 DA - 2022/01 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2021-0144 UR - https://global-sci.org/intro/article_detail/aamm/20206.html KW - Elliptic equations, optimal control, control-state constraints, a posteriori error estimates, $hp$ spectral element method. AB -

This paper investigates an optimal control problem governed by an elliptic equation with integral control and state constraints. The control problem is approximated by the $hp$ spectral element method with high accuracy and geometric flexibility. Optimality conditions of the continuous and discrete optimal control problems are presented, respectively. The a posteriori error estimates both for the control and state variables are established in detail. In addition, illustrative numerical examples are carried out to demonstrate the accuracy of theoretical results and the validity of the proposed method.