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A posteriori error analysis for nonconforming approximation of multiple eigenvalues
Author(s) -
Boffi Daniele,
Durán Ricardo G.,
Gardini Francesca,
Gastaldi Lucia
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3452
Subject(s) - mathematics , eigenvalues and eigenvectors , estimator , a priori and a posteriori , multiplicity (mathematics) , convergence (economics) , laplace transform , error analysis , finite element method , mathematical analysis , statistics , philosophy , physics , epistemology , quantum mechanics , economics , thermodynamics , economic growth
In this paper, we study an a posteriori error indicator introduced in E. Dari, R.G. Durán, and C. Padra, Appl. Numer. Math ., 2012, for the approximation of the Laplace eigenvalue problem with Crouzeix–Raviart nonconforming finite elements. In particular, we show that the estimator is robust also in presence of eigenvalues of multiplicity greater than one. Some numerical examples confirm the theory and illustrate the convergence of an adaptive algorithm when dealing with multiple eigenvalues. Copyright © 2015 John Wiley & Sons, Ltd.