Upper spectral bounds and a posteriori error analysis of several mixed finite element approximations for the Stokes eigenvalue problem

被引：0
|
作者：
YANG YiDu [1 ]
JIANG Wei [2 ]
机构：
[1] School of Mathematics and Computer Science, Guizhou Normal University
[2] School of Physics and Mechanical & Electrical Engineering, Xiamen University
来源：
Science China(Mathematics) | 2013年 / 56卷 / 06期
基金：
中国国家自然科学基金;
关键词：
the Stokes eigenvalue; conforming mixed finite elements; upper spectral bounds; a posteriori error estimates;
D O I：
暂无
中图分类号：
O241.82 [偏微分方程的数值解法];
学科分类号：
070102 ;
摘要：
This paper discusses conforming mixed finite element approximations for the Stokes eigenvalue problem. Firstly, several mixed finite element identities are proved. Based on these identities, the following new results are given: (1) It is proved that the numerical eigenvalues obtained by mini-element, P1-P1 element and Q1-Q1 element approximate the exact eigenvalues from above. (2) As for the P1-P1 , Q1-Q1 and Q1-P0 element eigenvalues, the asymptotically exact a posteriori error indicators are presented. (3) The reliable and efficient a posteriori error estimator proposed by Verfürth is applied to mini-element eigenfunctions. Finally, numerical experiments are carried out to verify the theoretical analysis.
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页码：1308 / 1325
页数：18
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