TY - JOUR
T1 - Lower Bounds of Eigenvalues of the Stokes  Operator  by Nonconforming Finite Elements on Local Quasi-Uniform Grids
AU - Li , Youai
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 - <p style="text-align: justify;">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.</p>