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 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.2011.48.5.1079Printed 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 Downloads: Full-text PDF