@Article{AAMM-8-464, author = {Fenglin and Huang and and 19685 and and Fenglin Huang and Yanping and Chen and and 19686 and and Yanping Chen and Xiulian and Shi and and 19687 and and Xiulian Shi}, title = {Equivalent a Posteriori Error Estimator of Spectral Approximation for Control Problems with Integral Control-State Constraints in One Dimension}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {3}, pages = {464--484}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m591}, url = {http://global-sci.org/intro/article_detail/aamm/12098.html} }