Local and Parallel Finite Element Algorithms Based on Two-Grid Discretization for Steady Navier-Stokes Equations

MA Fei-yao; MA Yi-chen; WO Wei-feng

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(1): 25-33

MA Fei-yao, MA Yi-chen, WO Wei-feng. Local and Parallel Finite Element Algorithms Based on Two-Grid Discretization for Steady Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2007, 28(1): 25-33.

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Local and Parallel Finite Element Algorithms Based on Two-Grid Discretization for Steady Navier-Stokes Equations

1.
College of Science, Xi'an Jiaotong University, Xi'an 710049, P. R. China;

Received Date: 2006-03-30
Rev Recd Date: 2006-10-31
Publish Date: 2007-01-15

Abstract

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 it drops the coarse solution of the region near the boundary. At last, by overlapping domain decomposition, the parallel algorithms are obtained. The error of these algorithms are analyzed and some error estimates are got which are better than that 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 highly efficient.
- Navier-Stokes equation,
- finite element method,
- two-grid,
- local,
- parallel

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References(9)

References

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