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.
Youngmi Choi, Sangdong Kim, and Hyung-Chun Lee
Ajou University, Kyungpook National University, Ajou University
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
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