@Article{AAMM-14-469,
author = {Zhang , JinlingChen , YanpingHuang , Yunqing and Huang , Fenglin},
title = {A Posteriori Error Estimates for $hp$ Spectral Element Approximation of Elliptic Control Problems with Integral Control and State Constraints},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2022},
volume = {14},
number = {2},
pages = {469--493},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0144},
url = {http://global-sci.org/intro/article_detail/aamm/20206.html}
}