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Title: Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations (English)
Author: Li, Qin
Author: Lin, Qun
Author: Xie, Hehu
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 58
Issue: 2
Year: 2013
Pages: 129-151
Summary lang: English
Category: math
Summary: The paper deals with error estimates and lower bound approximations of the Steklov eigenvalue problems on convex or concave domains by nonconforming finite element methods. We consider four types of nonconforming finite elements: Crouzeix-Raviart, $Q_{1}^{\rm rot}$, $EQ_{1}^{\rm rot}$ and enriched Crouzeix-Raviart. We first derive error estimates for the nonconforming finite element approximations of the Steklov eigenvalue problem and then give the analysis of lower bound approximations. Some numerical results are presented to validate our theoretical results. (English)
Keyword: Steklov eigenvalue problem
Keyword: nonconforming finite element
Keyword: error estimate
Keyword: lower bound of the eigenvalues
MSC: 35A35
MSC: 35J25
MSC: 35P10
MSC: 35P15
MSC: 65N12
MSC: 65N15
MSC: 65N25
MSC: 65N30
idZBL: Zbl 1274.65296
idMR: MR3034819
DOI: 10.1007/s10492-013-0007-5
Date available: 2013-03-01T15:50:20Z
Last updated: 2020-07-02
Stable URL:
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