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Volume 10, Issue 3
Spectral Method Approximation of Flow Optimal Control Problems with $H^1$-Norm State Constraint

Yanping Chen & Fenglin Huang

Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 614-638.

Published online: 2017-10

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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.

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@Article{NMTMA-10-614, author = {}, title = {Spectral Method Approximation of Flow Optimal Control Problems with $H^1$-Norm State Constraint}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2017}, volume = {10}, number = {3}, pages = {614--638}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.m1419}, url = {http://global-sci.org/intro/article_detail/nmtma/12361.html} }
TY - JOUR T1 - Spectral Method Approximation of Flow Optimal Control Problems with $H^1$-Norm State Constraint JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 614 EP - 638 PY - 2017 DA - 2017/10 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.m1419 UR - https://global-sci.org/intro/article_detail/nmtma/12361.html KW - AB -

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.

Yanping Chen & Fenglin Huang. (2020). Spectral Method Approximation of Flow Optimal Control Problems with $H^1$-Norm State Constraint. Numerical Mathematics: Theory, Methods and Applications. 10 (3). 614-638. doi:10.4208/nmtma.2017.m1419
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