A Posteriori Error Estimates for $hp$ Spectral Element Approximation of Elliptic Control Problems with Integral Control and State Constraints (Advances in Applied Mathematics and Mechanics, 2022)
This paper investigates an optimal control problem governed by an ellipticequation 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 problemsare presented, respectively. The a posteriori error estimates both for the control andstate variables are established in detail. In addition, illustrative numerical examplesare carried out to demonstrate the accuracy of theoretical results and the validity ofthe proposed method.