Asymptotic error expansion and Richardson extrapolation of eigenvalue approximations for second order elliptic problems by the mixed finite element method
type: Item
instance of: scholarly article
title: Asymptotic error expansion and Richardson extrapolation of eigenvalue approximations for second order elliptic problems by the mixed finite element method
zbMATH Open document ID: 1201.65202
author: Qun Lin
author: Hehu Xie
published in: Applied Numerical Mathematics
publication date: 2009-07-02T00:00:00Z
review text: The paper is concerned with symmetric Neumann eigenvalue problems for second-order elliptic differential operators. The problem is formulated as a saddle-point problem, and a mixed finite element scheme is considered for its numerical solution. The eigenvalue error is represented in terms of the exact solution and its finite element interpolant. Based on this representation, an asymptotic expansion of the eigenvalue error is obtained, which is used to derive an extrapolation scheme. Three numerical examples, one of them on an \(L\)-shaped domain, are presented to illustrate the results.
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 65B99
zbMATH DE Number: 5574504
zbMATH Keywords: second order elliptic eigenvalue problem
zbMATH Keywords: mixed finite element method
zbMATH Keywords: asymptotic error expansion
zbMATH Keywords: Richardson extrapolation
zbMATH Keywords: Raviart-Thomas element
reviewed by: Michael Plum
MaRDI profile type: Publication
full work available at URL: j.apnum.2009.01.011
OpenAlex ID: W2058400338
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Wikidata QID: Q112880212
DOI: 10.1016/J.APNUM.2009.01.011
description: scientific article; zbMATH DE number 5574504