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

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 is 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.

65N30, 65N15, 35J25

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@Article{AAMM-11-241, author = {}, 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 is 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} }
TY - JOUR T1 - Lower Bounds of Eigenvalues of the Stokes Operator by Nonconforming Finite Elements on Local Quasi-Uniform Grids JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 241 EP - 254 PY - 2019 DA - 2019/01 SN - 11 DO - http://doi.org/10.4208/aamm.OA-2018-0061 UR - https://global-sci.org/intro/article_detail/aamm/12930.html KW - Lower bound, eigenvalue, nonconforming finite element method, Stokes operator. AB -

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.

Youai Li. (2020). Lower Bounds of Eigenvalues of the Stokes Operator by Nonconforming Finite Elements on Local Quasi-Uniform Grids. Advances in Applied Mathematics and Mechanics. 11 (1). 241-254. doi:10.4208/aamm.OA-2018-0061
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