Generalized Rayleigh quotient and finite element two-grid discretization schemes
type: Item
instance of: scholarly article
title: Generalized Rayleigh quotient and finite element two-grid discretization schemes
zbMATH Open document ID: 1188.65151
published in: Science in China. Series A
publication date: 2009-12-11T00:00:00Z
review text: This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) The Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of the exact eigenvalue with the ascent of the finite element approximate eigenvalue. 3) Based on the work of \textit{J. Xu} and \textit{A. Zhou} [Math. Comput. 70, No. 233, 17--25 (2001; Zbl 0959.65119)], finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and nonconforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.
reviewed by: Wilhelm Heinrichs
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 5645737
zbMATH Keywords: nonselfadjoint elliptic eigenvalue problem
zbMATH Keywords: finite elements
zbMATH Keywords: generalized Rayleigh quotient
zbMATH Keywords: two-grid discretization scheme
author: Yidu Yang
author: Xinyue Fan
MaRDI profile type: Publication
full work available at URL: s11425-009-0016-8
OpenAlex ID: W2047742486
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DOI: 10.1007/S11425-009-0016-8
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description: scientific article; zbMATH DE number 5645737