Convergence of the Newton's method for an optimal control problems for Navier-Stokes equations
Bull. Korean Math. Soc. 2011 Vol. 48, No. 5, 1079-1092
https://doi.org/10.4134/BKMS.2011.48.5.1079
Printed September 1, 2011
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
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