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 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.