Lower Bounds of Eigenvalues of the Stokes Operator by Nonconforming Finite Elements on Local Quasi-Uniform Grids
Year: 2019
Author: Youai Li
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 1 : pp. 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 is a novel and sharp $L^2$ error estimate of discrete eigenfunctions, and a new error analysis of nonconforming finite element methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0061
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 1 : pp. 241–254
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Lower bound eigenvalue nonconforming finite element method Stokes operator.