A Posteriori Error Estimates for $hp$ Spectral Element Approximation of Elliptic Control Problems with Integral Control and State Constraints
Year: 2022
Author: Jinling Zhang, Yanping Chen, Yunqing Huang, Fenglin Huang
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 2 : pp. 469–493
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0144
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 2 : pp. 469–493
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Elliptic equations optimal control control-state constraints a posteriori error estimates $hp$ spectral element method.