A Two-Level Stabilized Finite Element Method for the Stokes Eigenvalue Problem

HUANG Peng-zhan; HE Yin-nian; FENG Xin-long

doi:10.3879/j.issn.1000-0887.2012.05.007

Volume 33 Issue 5

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HUANG Peng-zhan, HE Yin-nian, FENG Xin-long. A Two-Level Stabilized Finite Element Method for the Stokes Eigenvalue Problem[J]. Applied Mathematics and Mechanics, 2012, 33(5): 588-597. doi: 10.3879/j.issn.1000-0887.2012.05.007

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A Two-Level Stabilized Finite Element Method for the Stokes Eigenvalue Problem

doi: 10.3879/j.issn.1000-0887.2012.05.007

¹College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P.R.China;²Center for Computational Geosciences, School of Mathematics and Statistics, Xi′an Jiaotong University, Xi’an 710049, P.R.China

Received Date: 2011-05-04
Rev Recd Date: 2012-02-10
Publish Date: 2012-05-15

Abstract

Abstract

A two-level stabilized finite element method for the Stokes eigenvalue problem based on local Gauss integration was considered. The method involved solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h=O(H²), which can still maintain an asymptotically optimal accuracy. The given method provided an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involved solving a Stokes eigenvalue problem on a fine mesh with mesh size h.Hence, the method can save a large amount of computational time. Moreover, numerical tests confirmed the theoretical results of the presented method.
- Stokes eigenvalue problem,
- stabilized method,
- lowest equal-order pair,
- two-level method

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References

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