@Article{CiCP-7-738,
author = {Soorok Ryu, Sang Dong Kim and Hyung-Chun Lee},
title = {First-Order System Least-Squares Methods for a Flux Control Problem by the Stokes Flow},
journal = {Communications in Computational Physics},
year = {2010},
volume = {7},
number = {4},
pages = {738--758},
abstract = {<p style="text-align: justify;">This article deals with a first-order least-squares approach to the solution of
an optimal control problem governed by Stokes equations. As with our earlier work
on a velocity control by the Stokes flow in [S. Ryu, H.-C. Lee and S. D. Kim, SIAM
J. Numer. Anal., 47 (2009), pp. 1524-1545], we recast the objective functional as a H<sup>1&nbsp;</sup>seminorm in the velocity control term. By introducing a velocity-flux variable and using
the Lagrange multiplier rule, a first-order optimality system is obtained. We show that
the least-squares principle based on L<sup>2</sup> norms applied to this system yields the optimal
discretization error estimates for each variable in H<sup>1</sup> norm, including the velocity flux.
For numerical tests, multigrid method is employed to the discrete algebraic system, so
that the velocity and flux controls are obtained.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.2009.09.067},
url = {http://global-sci.org/intro/article_detail/cicp/7652.html}
}