An error estimator for spectral method approximation of flow control with state constraint-Reference-Cited by-同舟云学术

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

Published:2022 Issue:9 Volume:30 Page:3193-3210
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Huang Fenglin¹,Chen Yanping²,Lin Tingting¹

Affiliation:

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

Abstract

<abstract><p>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 <italic>hp</italic> spectral element approximation for flow control in the future work.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference18 articles.

1. E. Casas, Control of an elliptic problem with pointwise state constraints, SIAM J. Control Optim., 24 (1986), 1309–1318. https://doi.org/10.1137/0324078

2. E. Casas, Boundary control of semilinear elliptic equations with pointwise state constraints, SIAM J. Control Optim., 31 (1993), 993–1006. https://doi.org/10.1137/0331044

3. F. Tröltzsch, Optimal Control of Partial Differential Equations. Theory, Methods, and Applications, Grad. Stud. Math. 112, American Mathematical Society, Providence, RI, 2010.

4. O. Benedix, B. Vexler, A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints, Comput. Optim. Appl., 44 (2009), 3–25. https://doi.org/10.1007/s10589-008-9200-y

5. W. Liu, D. Yang, L. Yuan, C. Ma, Finite elemtnt approximations of an optimal control problem with integral state constraint, SIAM J. Numer. Anal., 48 (2010), 1163–1185. https://doi.org/10.1137/080737095