Volume 11, Issue 1
Lower Bounds of Eigenvalues of the Stokes Operator by Nonconforming Finite Elements on Local Quasi-Uniform Grids

Youai Li

Adv. Appl. Math. Mech., 11 (2019), pp. 241-254.

Published online: 2019-01

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  • Abstract

This paper is a generalization of  some recent results concerned with the  lower bound property of eigenvalues produced by both the  enriched rotated $Q_1$ and Crouzeix--Raviart elements of the Stokes eigenvalue problem. The main ingredient are  a novel and sharp $L^2$ error estimate of discrete eigenfunctions,  and   a new error analysis of nonconforming  finite element methods.


  • Keywords

Lower bound eigenvalue nonconforming finite element method Stokes operator.

  • AMS Subject Headings

65N30 65N15 35J25

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COPYRIGHT: © Global Science Press

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@Article{AAMM-11-241, author = {Youai Li}, title = {Lower Bounds of Eigenvalues of the Stokes Operator by Nonconforming Finite Elements on Local Quasi-Uniform Grids}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {1}, pages = {241--254}, abstract = {

This paper is a generalization of  some recent results concerned with the  lower bound property of eigenvalues produced by both the  enriched rotated $Q_1$ and Crouzeix--Raviart elements of the Stokes eigenvalue problem. The main ingredient are  a novel and sharp $L^2$ error estimate of discrete eigenfunctions,  and   a new error analysis of nonconforming  finite element methods.


}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0061}, url = {http://global-sci.org/intro/article_detail/aamm/12930.html} }
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