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Stability and convergence of optimum spectral non-linear Galerkin methods

✍ Scribed by He Yinnian; Hou Yanren; Li Kaitai

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
205 KB
Volume
24
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

Our objective in this article is to present some numerical schemes for the approximation of the 2‐D Navier–Stokes equations with periodic boundary conditions, and to study the stability and convergence of the schemes. Spatial discretization can be performed by either the spectral Galerkin method or the optimum spectral non‐linear Galerkin method; time discretization is done by the Euler scheme and a two‐step scheme. Our results show that under the same convergence rate the optimum spectral non‐linear Galerkin method is superior to the usual Galerkin methods. Finally, numerical example is provided and supports our results. Copyright © 2001 John Wiley & Sons, Ltd.

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