ANALYSIS AND COMPUTATIONS OF LEAST-SQUARES METHOD FOR OPTIMAL CONTROL PROBLEMS FOR THE STOKES EQUATIONS

被引：3

作者：

Choi, Youngmi ^{[1
]}

Kim, Sang Dong ^{[2
]}

Lee, Hyung-Chun ^{[1
]}

机构：

[1] Ajou Univ, Dept Math, Suwon 443749, South Korea

[2] Kyungpook Natl Univ, Dept Math, Taegu 702701, South Korea

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2009年 / 46卷 / 05期

关键词：

optimal control; least-squares finite element method; multigrid method; stokes equations; FINITE-ELEMENT METHODS; STATIONARY BOUSSINESQ EQUATIONS; 1ST-ORDER ELLIPTIC-SYSTEMS; ONE INNER-PRODUCT; DIMENSIONS; OPTIMIZATION; APPROXIMATION; PRINCIPLES;

D O I：

10.4134/JKMS.2009.46.5.1007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

First-order least-squares method of a distributed optimal control problem for the incompressible Stokes equations is considered. An optimality system for the optimal solution are reformulated to the equivalent first-order system by introducing the vorticity and then the least-squares functional corresponding to the system is defined in terms of the sum of the squared H(-1) and L(2) norms of the residual equations of the system. Finite element approximations are studied and optimal error estimates are obtained. Resulting linear system of the optimality system is symmetric and positive definite. The V-cycle multigrid method is applied to the system to test computational efficiency.

引用

页码：1007 / 1025

页数：19

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