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 -

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.