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Equivalent a Posteriori Error Estimator of Spectral Approximation for Control Problems with Integral Control-State Constraints in One Dimension

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Existence theories

Published online by Cambridge University Press:  27 January 2016

Fenglin Huang ,
Yanping Chen  and
Xiulian Shi
Fenglin Huang
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
Xiulian Shi
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
*
*Corresponding author. Email: hfl_937@sina.com (F. L. Huang), yanpingchen@scnu.edu.cn (Y. P. Chen), pgny@163.com (X. L. Shi)
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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 indicatorwith explicit expression. Secondly, appropriate base functions of the discrete spacesmake 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 controlelliptic equationscontrol-state constraintsspectral methoda posteriori error estimator

MSC classification

Secondary: 49J20: Optimal control problems involving partial differential equations 65K15: Numerical methods for variational inequalities and related problems 65M12: Stability and convergence of numerical methods 65M70: Spectral, collocation and related methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 3 , June 2016 , pp. 464 - 484
Copyright
Copyright © Global-Science Press 2016 

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