TY - JOUR
T1 - Equivalent a Posteriori Error Estimator of Spectral Approximation for Control Problems with Integral Control-State Constraints in One Dimension
AU - Huang , Fenglin
AU - Chen , Yanping
AU - Shi , Xiulian
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 464
EP - 484
PY - 2018
DA - 2018/05
SN - 8
DO - http://doi.org/10.4208/aamm.2014.m591
UR - https://global-sci.org/intro/article_detail/aamm/12098.html
KW - Optimal control, elliptic equations, control-state constraints, spectral method, a posteriori error estimator.
AB - <p style="text-align: justify;">In this paper, we investigate the Galerkin spectral approximation for elliptic
control problems with integral control and state constraints. Firstly, an a posteriori error
estimator is established, which can be acted as the equivalent indicator with explicit
expression. Secondly, appropriate base functions of the discrete spaces make it probable
to solve the discrete system. Numerical test indicates the reliability and efficiency
of the estimator, and shows the proposed method is competitive for this class of control
problems. These discussions can certainly be extended to two- and three-dimensional
cases.</p>