Year: 2005
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 4 : pp. 459–478
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, $k \geq 1$. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-IJNAM-941
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 4 : pp. 459–478
Published online: 2005-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: nonlinear operator equation the Navier-Stokes equations Taylor expansion algorithm optimum nonlinear Galerkin method.