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Research Article | Open Access

An error estimator for spectral method approximation of flow control with state constraint

Fenglin Huang1( ), Yanping Chen2, Tingting Lin1
School of Mathematics and Statistics, Xinyang Normal University, No.237 Nanhu Road, Shihe District, Xinyang 464000, China
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
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Abstract

We consider the spectral approximation of flow optimal control problems with state constraint. The main contribution of this work is to derive an a posteriori error estimator, and show the upper and lower bounds for the approximation error. Numerical experiment shows the efficiency of the error indicator, which will be used to construct reliable adaptive hp spectral element approximation for flow control in the future work.

Keywords

spectral methodoptimal controlstate constraintstokes equationsupper and lower bounds

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Electronic Research Archive
Volume 30 Issue 9,
September 2022
Pages 3193-3210
DOI: 10.3934/era.2022162

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Cite this article:
Huang F, Chen Y, Lin T. An error estimator for spectral method approximation of flow control with state constraint. Electronic Research Archive, 2022, 30(9): 3193-3210. https://doi.org/10.3934/era.2022162

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Received: 07 March 2022
Revised: 17 May 2022
Accepted: 18 May 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)