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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2010; 47(1): 83-100

Printed January 1, 2010

https://doi.org/10.4134/JKMS.2010.47.1.83

Copyright © The Korean Mathematical Society.

A multigrid method for an optimal control problem of a diffusion-convection equation

Hunki Baek, Sang Dong Kim, and Hyung-Chun Lee

Kyungpook National University, Kyungpook National University, and Ajou University

Abstract

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In this article, an optimal control problem associated with convection-diffusion equation is considered. Using Lagrange multiplier, the optimality system is obtained. The derived optimal system becomes coupled, non-symmetric partial differential equations. For discretizations and implementations, the finite element multigrid $V$-cycle is employed. The convergence analysis of finite element multigrid methods for the derived optimal system is shown. Some numerical simulations are performed.

Keywords: optimal control problem, multigrid method, diffusion-convection equation

MSC numbers: Primary 49K20, 65N12, 65N30, 65N55

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