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Analysis and computations of least-squares method for optimal control problems for the Stokes equations

김상동|최영미|이형천
대한수학회 (The Korean Mathematical Society)|2009.09|대한수학회지 (Journal of the KMS)|제46권 제5호|pp. 1007-1025

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참고문헌

키워드

optimal controlmultigrid methodleast-squares finite element methodstokes equations
주제분류수학

초록

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.

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 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.

참고문헌 (28)

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