Two-level stabilized finite element method for Stokes eigenvalue problem

doi:10.1007/s10483-012-1575-7

Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (5): 621-630.doi: https://doi.org/10.1007/s10483-012-1575-7

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Two-level stabilized finite element method for Stokes eigenvalue problem

Peng-zhan HUANG¹, Yin-nian HE^2,1, Xin-longFENG¹

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

Received:2011-05-04 Revised:2012-02-10 Online:2012-05-10 Published:2012-05-10
Contact: Yin-nian HE, Professor, Ph.D., E-mail: heyn@mail.xjtu.edu.cn E-mail:heyn@mail.xjtu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 10901131, 10971166, and 10961024), the National High Technology Research and Development Program of China (No. 2009AA01A135), and the Natural Science Foundation of Xinjiang Uygur Autonomous Region (No. 2010211B04)

Abstract

Abstract:

A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves 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 the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.

Key words: Stokes eigenvalue problem, lowest equal-order pair, stabilized method, two-level method

2010 MSC Number:

Peng-zhan HUANG;Yin-nian HE;Xin-longFENG. Two-level stabilized finite element method for Stokes eigenvalue problem. Applied Mathematics and Mechanics (English Edition), 2012, 33(5): 621-630.

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Two-level stabilized finite element method for Stokes eigenvalue problem

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