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 - <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>