Applied Mathematics and Mechanics

, Volume 28, Issue 1, pp 27–35

# Local and parallel finite element algorithms based on two-grid discretization for steady Navier-Stokes equations

• Ma Fei-yao  (马飞遥)
• Ma Yi-chen  (马逸尘)
• Wo Wei-feng  (沃维丰)
Article

## Abstract

Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine finite element space on the subdomain. The local algorithm consists of finding a solution for a given nonlinear problem in the coarse finite element space and a solution for a linear problem in the fine finite element space, then droping the coarse solution of the region near the boundary. By overlapping domain decomposition, the parallel algorithms are obtained. This paper analyzes the error of these algorithms and gets some error estimates which are better than those of the standard finite element method. The numerical experiments are given too. By analyzing and comparing these results, it is shown that these algorithms are correct and high efficient.

## Key words

Navier-Stokes equations finite element method two-grid local parallel

O241.82

65N30 65N55

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© Editorial Committee of Appl. Math. Mech. 2007

## Authors and Affiliations

• Ma Fei-yao  (马飞遥)
• 1
Email author
• Ma Yi-chen  (马逸尘)
• 1
• Wo Wei-feng  (沃维丰)
• 2
1. 1.College of ScienceXi’an Jiaotong UniversityXi’anP. R. China
2. 2.Center for Nonlinear StudiesNorthwest UniversityXi’anP. R. China