Volume 2, Issue 4
Taylor Expansion Algorithm for the Branching Solution of the Navier-Stokes Equations

K. Li & Y. He

DOI:

Int. J. Numer. Anal. Mod., 2 (2005), pp. 459-478

Published online: 2005-02

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  • Abstract

The aim of this paper is to present a general algorithm for the branching solution of nonlinear operator equations in a Hilbert space, namely the k-order Taylor expansion algorithm, k >= 1. The standard Galerkin method can be viewed as the 1-order Taylor expansion algorithm; while the optimum nonlinear Galerkin method can be viewed as the 2-order Taylor expansion algorithm. The general algorithm is then applied to the study of the numerical approximations for the steady Navier-Stokes equations. Finally, the theoretical analysis and numerical experiments show that, in some situations, the optimum nonlinear Galerkin method provides higher convergence rate than the standard Galerkin method and the nonlinear Galerkin method.

  • Keywords

nonlinear operator equation the Navier-Stokes equations Taylor expansion algorithm optimum nonlinear Galerkin method

  • AMS Subject Headings

35Q10 47H 65N30 76D05

  • Copyright

COPYRIGHT: © Global Science Press

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