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

Fenglin Huang; Yanping Chen; Tingting Lin; Fenglin Huang; Yanping Chen; Tingting Lin

doi:10.3934/era.2022162

Electronic Research Archive

2022, Volume 30, Issue 9: 3193-3210. doi: 10.3934/era.2022162

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

1.
School of Mathematics and Statistics, Xinyang Normal University, No.237 Nanhu Road, Shihe District, Xinyang 464000, China
2.
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received: 07 March 2022 Revised: 17 May 2022 Accepted: 18 May 2022 Published: 20 June 2022

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.
- spectral method,
- optimal control,
- state constraint,
- stokes equations,
- upper and lower bounds
Citation: Fenglin Huang, Yanping Chen, Tingting Lin. An error estimator for spectral method approximation of flow control with state constraint[J]. Electronic Research Archive, 2022, 30(9): 3193-3210. doi: 10.3934/era.2022162

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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.

References

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