Eigenvalue approximation by mixed non-conforming finite element methods
type: Item
instance of: scholarly article
title: Eigenvalue approximation by mixed non-conforming finite element methods
zbMATH Open document ID: 1317.65229
author: Anahí Dello Russo
published in: Calcolo
publication date: 2015-03-23T00:00:00Z
review text: A theory for the approximation of eigenvalue problems in mixed form by non-conforming methods is given. The paper is organized as follows. Section 1 is an introduction. In Section 2, the statement of the eigenvalue problem is given. In Section 3, a set of sufficient conditions for having good convergence properties for the approximation of the eigenvalue/eigenvector pairs in the sense that the numerical method does not introduce spurious modes are given. In Section 4, this theory is applied to analyze the problem of determining the vibrational modes of a linear elastic structure using the classical Hellinger-Reissner mixed formulation. It is shown that a numerical method based on the lowest-order Arnold-Winther non-conforming space provides a spectrally correct approximation of the eigenvalue/eigenvector pairs. Optimal-order error estimates are proved, too.
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74S05
zbMATH DE Number: 6418690
zbMATH Keywords: spectral analysis
zbMATH Keywords: eigenvalue problems in mixed form
zbMATH Keywords: non-conforming finite element methods
zbMATH Keywords: linear elasticity equations
zbMATH Keywords: convergence
zbMATH Keywords: vibrational modes
zbMATH Keywords: Hellinger-Reissner mixed formulation
zbMATH Keywords: error estimate
reviewed by: Temur Jangveladze
MaRDI profile type: Publication
full work available at URL: s10092-013-0101-9
OpenAlex ID: W2097160699
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DOI: 10.1007/S10092-013-0101-9
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description: scientific article; zbMATH DE number 6418690