First-Order System Least-Squares Methods for an Optimal Control Problem by the Stokes Flow
作者： Soorok Ryu , Hyung-Chun Lee , Sang Dong Kim
DOI: 10.1137/070701157
关键词: Optimization problem 、 Mathematical analysis 、 Finite element method 、 Lagrange multiplier 、 Optimal control 、 Stokes flow 、 Mathematics 、 Algebraic number 、 Norm (mathematics) 、 Multigrid method
摘要: The least-squares approximations of an optimal control problem governed by the Stokes equations are considered, which leads to unconstrained coupled optimization Lagrange multiplier method. functionals for two- and three-dimensional first-order optimality systems employed modifying those in [Z. Cai, T. A. Manteuffel, S. F. McCormick, SIAM J. Numer. Anal., 34 (1997), pp. 1727-1741]. established ellipticity continuity a product $H^1$ norm yield discretization error estimates finite element spaces. For numerical tests, we apply V-cycle multigrid methods whole discrete algebraic system.
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