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

Spectral Method Approximation of Flow Optimal Control Problems with $H^1$-Norm State Constraint
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Year:    2017

Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2017.m1419

Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 3 : pp. 614–638

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:   

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