FIRST-ORDER SYSTEM LEAST-SQUARES METHODS FOR AN OPTIMAL CONTROL PROBLEM BY THE STOKES FLOW

被引：7

作者：

Ryu, Soorok ^{[1
]}

Lee, Hyung-Chun ^{[2
]}

Kim, Sang Dong ^{[3
]}

机构：

[1] Kyungpook Natl Univ, Dept Ind & Appl Math, Taegu 702701, South Korea

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

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

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2009年 / 47卷 / 02期

关键词：

optimal control; least-squares finite element methods; coupled Stokes equations; V-cycle; FINITE-ELEMENT METHODS; LINEAR ELASTICITY; ELLIPTIC-SYSTEMS; EQUATIONS; OPTIMIZATION; APPROXIMATION; PRINCIPLES; DIMENSIONS; BOUNDARY;

D O I：

10.1137/070701157

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The least-squares approximations of an optimal control problem governed by the Stokes equations are considered, which leads to an unconstrained coupled optimization problem by the Lagrange multiplier method. The least-squares functionals for the two- and three-dimensional first-order coupled optimality systems are employed by modifying those functionals in [Z. Cai, T. A. Manteuffel, and S. F. McCormick, SIAM J. Numer. Anal., 34 (1997), pp. 1727-1741]. The established ellipticity and continuity in a product H(1) norm yield the optimal discretization error estimates in the finite element spaces. For numerical tests, we apply V-cycle multigrid methods to the whole discrete algebraic system.

引用

页码：1524 / 1545

页数：22

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