@Article{NMTMA-10-614,
author = {Yanping Chen and Fenglin Huang},
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 = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2017.m1419},
url = {http://global-sci.org/intro/article_detail/nmtma/12361.html}
}