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Spectral Method Approximation of Flow Optimal Control Problems with H 1-Norm State Constraint

Published online by Cambridge University Press:  20 June 2017

Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
Fenglin Huang*
Affiliation:
School of Mathematics and Statistics, Xinyang Normal University, No.237 Nanhu Road, Shihe District, Xinyang 464000, China
*
*Corresponding author. Email addresses: yanpingchen@scnu.edu.cn (Y. P. Chen), hfl_937@sina.com (F. L. Huang)
*Corresponding author. Email addresses: yanpingchen@scnu.edu.cn (Y. P. Chen), hfl_937@sina.com (F. L. Huang)
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Abstract

In this paper, we consider an optimal control problem governed by Stokes equations with H 1-norm state constraint. The control problem is approximated by spectral method, which provides very accurate approximation with a relatively small number of unknowns. Choosing appropriate basis functions leads to discrete system with sparse matrices. We first present the optimality conditions of the exact and the discrete optimal control systems, then derive both a priori and a posteriori error estimates. Finally, an illustrative numerical experiment indicates that the proposed method is competitive, and the estimator can indicate the errors very well.

Type
Research Article
Copyright
Copyright © Global-Science Press 2017 

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