A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations II: Time Discretization
Year: 2004
Author: Yinnian He, Huanling Miao, Chunfeng Ren
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 1 : pp. 33–54
Abstract
In this article we consider the fully discrete two-level finite element Galerkin method for the two-dimensional nonstationary incompressible Navier-Stokes equations. This method consists in dealing with the fully discrete nonlinear Navier-Stokes problem on a coarse mesh with width $H$ and the fully discrete linear generalized Stokes problem on a fine mesh with width $h << H$. Our results show that if we choose $H=O(h^{1/2}$) this method is as the same stability and convergence as the fully discrete standard finite element Galerkin method which needs dealing with the fully discrete nonlinear Navier-Stokes problem on a fine mesh with width $h$. However, our method is cheaper than the standard fully discrete finite element Galerkin method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-JCM-8849
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 1 : pp. 33–54
Published online: 2004-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Navier-Stokes equations Galerkin method Finite element.