A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations I: Spatial Discretization
Year: 2004
Author: Yinnian He
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 1 : pp. 21–32
Abstract
In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a $H^1$-optimal velocity approximation and a $L_2$-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small, nonlinear Navier-Stokes problem on the coarse mesh with mesh size $H$, one linear Stokes problem on the fine mesh with mesh size $h << H$. The algorithm we study produces an approximate solution with the optimal, asymptotic in $h$, accuracy.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-JCM-8848
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 1 : pp. 21–32
Published online: 2004-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Navier-Stokes equations Mixed finite element Error estimate Finite element method.