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Explicit lower bounds for Stokes eigenvalue problems by using nonconforming finite elements
Xie, Manting1; Xie, Hehu2,3; Liu, Xuefeng4
2018-03-01
Source PublicationJAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
ISSN0916-7005
Volume35Issue:1Pages:335-354
AbstractAn 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.
KeywordStokes eigenvalue problem Eigenvalue bound Crouzeix-Raviart element Enriched Crouzeix-Raviart element Explicit lower bound
DOI10.1007/s13160-017-0291-7
Language英语
Funding ProjectNational Science Foundations of China[NSFC 91730302] ; National Science Foundations of China[11771434] ; National Science Foundations of China[91330202] ; National Science Foundations of China[11371026] ; Science Challenge Project[TZ2016002] ; National Center for Mathematics and Interdisciplinary Science, CAS ; Japan Society for the Promotion of Science[26800090] ; Japan Society for the Promotion of Science[16H03950]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000426279600016
PublisherSPRINGER JAPAN KK
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29604
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
GB/T 7714
Xie, Manting,Xie, Hehu,Liu, Xuefeng. Explicit lower bounds for Stokes eigenvalue problems by using nonconforming finite elements[J]. JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS,2018,35(1):335-354.
APA Xie, Manting,Xie, Hehu,&Liu, Xuefeng.(2018).Explicit lower bounds for Stokes eigenvalue problems by using nonconforming finite elements.JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS,35(1),335-354.
MLA Xie, Manting,et al."Explicit lower bounds for Stokes eigenvalue problems by using nonconforming finite elements".JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 35.1(2018):335-354.
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