Treffer: Finite element approximation of the Neumann eigenvalue problem in domains with multiple cracks
Title:
Finite element approximation of the Neumann eigenvalue problem in domains with multiple cracks
Authors:
Contributors:
Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques (LAMA), Université Savoie Mont Blanc (USMB Université de Savoie Université de Chambéry )-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
Source:
IMA Journal of Numerical Analysis. 26:790-810
Publisher Information:
Oxford University Press (OUP), 2006.
Publication Year:
2006
Subject Terms:
domains with cracks, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, numerical examples, Finite element methods applied to problems in solid mechanics, finite element method, Estimates of eigenvalues in context of PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, 01 natural sciences, error estimates, 0103 physical sciences, [MATH]Mathematics [math], 0101 mathematics, Neumann-Laplacian eigenvalue problem
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Language:
English
ISSN:
1464-3642
0272-4979
0272-4979
DOI:
10.1093/imanum/drl002
Access URL:
Accession Number:
edsair.doi.dedup.....cd9de9459894e33a3bdbcc4ea974723e
Database:
OpenAIRE
Weitere Informationen
Summary: We study the Neumann-Laplacian eigenvalue problem in domains with multiple cracks. We derive a mixed variational formulation which holds on the whole geometric domain (including the cracks) and implements efficient finite-element discretizations for the computation of eigenvalues. Optimal error estimates are given and several numerical examples are presented, confirming the efficiency of the method. As applications, we numerically investigate the behaviour of the low eigenvalues in domains with a large number of cracks.