Explicit lower bounds for Stokes eigenvalue problems by using nonconforming finite elements

被引：14

作者：

Xie, Manting ^{[1
]}

Xie, Hehu ^{[2
,3
]}

Liu, Xuefeng ^{[4
]}

机构：

[1] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China

[3] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[4] Niigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata, Niigata 9502181, Japan

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2018年 / 35卷 / 01期

基金：

日本学术振兴会;

关键词：

Stokes eigenvalue problem; Eigenvalue bound; Crouzeix-Raviart element; Enriched Crouzeix-Raviart element; Explicit lower bound; A-POSTERIORI; APPROXIMATION; EIGENMODES; EQUATIONS; DOMAIN;

D O I：

10.1007/s13160-017-0291-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An algorithm is proposed to give explicit lower bounds of the Stokes eigenvalues by utilizing two nonconforming finite element methods: Crouzeix-Raviart (CR) element and enriched Crouzeix-Raviart (ECR) element. Compared with the existing literatures which give lower eigenvalue bounds under the asymptotic condition that the mesh size is "small enough", the proposed algorithm in this paper drops the asymptotic condition and provide explicit lower bounds even for a rough mesh. Numerical experiments are also performed to validate the theoretical results.

引用

页码：335 / 354

页数：20

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