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

Two-level stabilized finite element method for Stokes eigenvalue problem

黄鹏展¹, 何银年^2,1, 冯新龙¹

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

收稿日期:2011-05-04 修回日期:2012-02-10 出版日期:2012-05-10 发布日期:2012-05-10
通讯作者: Yin-nian HE, Professor, Ph.D., E-mail: heyn@mail.xjtu.edu.cn E-mail:heyn@mail.xjtu.edu.cn
基金资助:
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)

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)

摘要/Abstract

摘要：

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.

关键词: Stokes eigenvalue problem, stabilized method, lowest equal-order pair, two-level method

Abstract:

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

中图分类号:

黄鹏展;何银年;冯新龙. Two-level stabilized finite element method for Stokes eigenvalue problem[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(5): 621-630.

Peng-zhan HUANG;Yin-nian HE;Xin-longFENG. Two-level stabilized finite element method for Stokes eigenvalue problem[J]. 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

Two-level stabilized finite element method for Stokes eigenvalue problem

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