Year: 2010
Communications in Computational Physics, Vol. 7 (2010), Iss. 4 : pp. 738–758
Abstract
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 H1 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 L2 norms applied to this system yields the optimal discretization error estimates for each variable in H1 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.2009.09.067
Communications in Computational Physics, Vol. 7 (2010), Iss. 4 : pp. 738–758
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21