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

Title & Authors
ANALYSIS AND COMPUTATIONS OF LEAST-SQUARES METHOD FOR OPTIMAL CONTROL PROBLEMS FOR THE STOKES EQUATIONS
Choi, Young-Mi; Kim, Sang-Dong; Lee, Hyung-Chun;

Abstract
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 $\small{H^{-1}}$ and $\small{L^2}$ 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.
Keywords
optimal control;least-squares finite element method;multigrid method;stokes equations;
Language
English
Cited by
1.
ANALYSIS OF VELOCITY-FLUX FIRST-ORDER SYSTEM LEAST-SQUARES PRINCIPLES FOR THE OPTIMAL CONTROL PROBLEMS FOR THE NAVIER-STOKES EQUATIONS,;;

Journal of the Korea Society for Industrial and Applied Mathematics, 2010. vol.14. 2, pp.125-140
2.
FINITE ELEMENT APPROXIMATIONS OF THE OPTIMAL CONTROL PROBLEMS FOR STOCHASTIC STOKES EQUATIONS,;;;

대한수학회보, 2014. vol.51. 3, pp.847-862
1.
FINITE ELEMENT APPROXIMATIONS OF THE OPTIMAL CONTROL PROBLEMS FOR STOCHASTIC STOKES EQUATIONS, Bulletin of the Korean Mathematical Society, 2014, 51, 3, 847
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