Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2011; 48(5): 1079-1092

Printed September 1, 2011

https://doi.org/10.4134/BKMS.2011.48.5.1079

Copyright © The Korean Mathematical Society.

Convergence of the Newton's method for an optimal control problems for Navier-Stokes equations

Youngmi Choi, Sangdong Kim, and Hyung-Chun Lee

Ajou University, Kyungpook National University, Ajou University

Abstract

We consider the Newton's method for an direct solver of the optimal control problems of the Navier-Stokes equations. We show that the finite element solutions of the optimal control problem for Stokes equations may be chosen as the initial guess for the quadratic convergence of Newton's algorithm applied to the optimal control problem for the Navier-Stokes equations provided there are sufficiently small mesh size $h$ and the moderate Reynold's number.

Keywords: Navier-Stokes equations, optimal control, convergence, finite element method, Newton's method

MSC numbers: 65N30, 49K20