Volume 8, Issue 3
Equivalent a Posteriori Error Estimator of Spectral Approximation for Control Problems with Integral Control-State Constraints in One Dimension

Fenglin Huang, Yanping Chen & Xiulian Shi

Adv. Appl. Math. Mech., 8 (2016), pp. 464-484.

Published online: 2018-05

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  • 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 is 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.

  • Keywords

Optimal control, elliptic equations, control-state constraints, spectral method, a posteriori error estimator.

  • AMS Subject Headings

49J20, 65K15, 65M12, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-464, author = {}, 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 is 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} }
TY - JOUR T1 - Equivalent a Posteriori Error Estimator of Spectral Approximation for Control Problems with Integral Control-State Constraints in One Dimension 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 -

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 is 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.

Fenglin Huang, Yanping Chen & Xiulian Shi. (2020). Equivalent a Posteriori Error Estimator of Spectral Approximation for Control Problems with Integral Control-State Constraints in One Dimension. Advances in Applied Mathematics and Mechanics. 8 (3). 464-484. doi:10.4208/aamm.2014.m591
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