First-Order System Least-Squares Methods for a Flux Control Problem by the Stokes Flow

作     者：Soorok Ryu Sang Dong Kim Hyung-Chun Lee 

作者机构：Department of Industrial and Applied MathematicsKyungpook National UniversityDaegu 702-701Korea Department of MathematicsKyungpook National UniversityDaegu 702-701Korea Department of MathematicsAjou UniversitySuwon 443-749Korea 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2010年第7卷第4期

页      面：738-758页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work was supported by Korea Research Foundation under grant KRF-2005-070-C00017 

主　　题：Optimal control optimization least-squares finite element methods Lagrange multiplier Stokes equations. 

摘      要：This article deals with a first-order least-squares approach to the solution of an optimal control problem governed by Stokes *** with our earlier work on a velocity control by the Stokes flow in[***,H.-*** and ***,SIAM ***.,47(2009),pp.1524-1545],we recast the objective functional as a H1 seminorm in the velocity control *** introducing a velocity-flux variable and using the Lagrange multiplier rule,a first-order optimality system is *** 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 *** numerical tests,multigrid method is employed to the discrete algebraic system,so that the velocity and flux controls are obtained.