Convergence of the Newton's method for an optimal control problems for Navier-Stokes equations
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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.
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.
참고문헌 (8)
- P. B. Bochev, "Analysis of velocity-flux first-order system least-squares principles for the Navier-Stokes equations. I", SIAM J. Numer. Anal, 35(3), pp.990~1009 (1998)
- F. Brezzi, "Finite-dimensional approximation of nonlinear problems. I. Branches of nonsingular solutions", Numer. Math, 36(1), pp.1~25 (1980)
- P. Ciarlet, "Finite Element Method for Elliptic Problems" (1978), North-Holland
- V. Girault, "Finite Element Methods for Navier-Stokes Equations" (1986), Springer
- S. D. Kim, "Newton's method for the Navier-Stokes equations with finite-element initial guess of Stokes equations", COMPUTERS & MATHEMATICS WITH APPLICATIONS, 51(5), pp.805~816 (2006), PERGAMON-ELSEVIER SCIENCE LTD
- D. A. Knoll, "On Newton-Krylov multigrid methods for the incom- pressible Navier-Stokes equations", J. Comput. Phys, 163, pp.262~267 (2000)
- D. A. Knoll, "A multigrid preconditioned Newton-Krylov method", SIAM J. Sci. Comput, 21(2), pp.691~710 (1999)
- M. Pernice, "A multigrid-preconditioned Newton-Krylov Method for the incompressible Navier-Stokes equations", SIAM J. Sci. Comput, 23(2), pp.398~418 (2001)