A least-squares/penalty method for distributed optimal control problems for Stokes equations

Authors:
Youngmi Choi;Hyung-Chun Lee;Byeong-Chun Shin
Affiliations:
Department of Mathematics, Ajou University, Suwon 443-749, Republic of Korea;Department of Mathematics, Ajou University, Suwon 443-749, Republic of Korea;Department of Mathematics, Chonnam National University, Kwangju 500-757, Republic of Korea
Venue:
Computers & Mathematics with Applications
Year:
2007

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Abstract

The purpose of this paper is to construct an unconstrained optimal control problem by using a least-squares approach for the constrained distributed optimal control problem associated with incompressible Stokes equations. The constrained equations are reformulated to the equivalent first-order system by introducing vorticity, and then the least-squares functional corresponding to the system is enforced via a penalty term to the objective functional. The existence of a solution of the unconstrained optimal control problem is proved, and the convergence of this solution to that of unpenalized one is demonstrated as the penalty parameter tends to zero. Finite element approximations with error estimates are studied, and the relevant computational experiments are presented.