Correction of finite element eigenvalues for problems with natural or periodic boundary conditions
type: Item
instance of: scholarly article
title: Correction of finite element eigenvalues for problems with natural or periodic boundary conditions
zbMATH Open document ID: 0646.65070
DOI: 10.1007/BF01934090
published in: BIT
publication date: 1988-01-01T00:00:00Z
review text: Let \(\lambda_ 1,\lambda_ 2,..\). denote the eigenvalues of the Sturm- Liouville problem \(-y''+qy=\lambda y\), \(\delta_ 1y'(0)+\sigma_ 2y(0)=\sigma_ 3y'(\pi)+\sigma_ 4y(\pi)=0.\) For the case of natural and periodic boundary conditions and a finite element approximation on a uniform mesh of width \(h=\pi /n\) an asymptotic correction technique, developed by \textit{J. W. Paine}, \textit{F. R. de Hoog} and \textit{R. S. Anderssen} [Computing 26, 123-139 (1981; Zbl 0436.65063)] reduces the error of the approximation of \(\lambda_ k\) from \(O(k^ 4h^ 2)\) to \(O(kh^ 2)\). As numerical results show, the new technique is useful already for low values of k.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 34L99
zbMATH DE Number: 4054957
zbMATH Keywords: asymptotic correction
zbMATH Keywords: finite element method
zbMATH Keywords: natural boundary conditions
zbMATH Keywords: periodic boundary conditions
zbMATH Keywords: eigenvalues
zbMATH Keywords: Sturm-Liouville problem
author: Alan L. Andrew
reviewed by: Ludwig Elsner
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4054957