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CONVERGENCE OF THE NEWTON`S METHOD FOR AN OPTIMAL CONTROL PROBLEMS FOR NAVIER-STOKES EQUATIONS
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 Title & Authors
CONVERGENCE OF THE NEWTON`S METHOD FOR AN OPTIMAL CONTROL PROBLEMS FOR NAVIER-STOKES EQUATIONS
Choi, Young-Mi; Kim, Sang-Dong; Lee, Hyung-Chun;
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 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 Stoke 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;
 Language
English
 Cited by
 References
1.
P. B. Bochev, Z. Cai, T. A. Manteuffel, and S. F. McCormick, Analysis of velocity-ux first-order system least-squares principles for the Navier-Stokes equations. I, SIAM J. Numer. Anal. 35 (1998), no. 3, 990-1009. crossref(new window)

2.
F. Brezzi, J. Rappaz, and P. A. Raviart, Finite-dimensional approximation of nonlinear problems. I. Branches of nonsingular solutions, Numer. Math. 36 (1980/81), no. 1, 1-25.

3.
P. Ciarlet, Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.

4.
V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer, Berlin, 1986.

5.
S. D. Kim, Y. H. Lee, and B. C. Shin, Newton's method for the Navier-Stokes equations with finite-element initial guess of Stokes equations, Comput. Math. Appl. 51 (2006), no. 5, 805-816. crossref(new window)

6.
D. A. Knoll and V. A. Mousseau, On Newton-Krylov multigrid methods for the incom- pressible Navier-Stokes equations, J. Comput. Phys. 163 (2000), 262-267. crossref(new window)

7.
D. A. Knoll and W. Rider, A multigrid preconditioned Newton-Krylov method, SIAM J. Sci. Comput. 21 (1999), no. 2, 691-710. crossref(new window)

8.
M. Pernice and M. D. Tocci, A multigrid-preconditioned Newton-Krylov Method for the incompressible Navier-Stokes equations, SIAM J. Sci. Comput. 23 (2001), no. 2, 398-418. crossref(new window)