Finite element approximation of the Neumann eigenvalue problem in domains with multiple cracks |
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Authors: | Belhachmi, Zakaria Bucur, Dorin Sac-Epee, Jean-Marc |
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Affiliation: | Département de Mathématiques, UMR-CNRS 7122 Université de Metz Ile du Saulcy,57045 Metz Cedex 01, France |
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Abstract: | ** Email: belhach{at}poncelet.univ-metz.fr*** Email: bucur{at}math.univ-metz.fr**** Email: jmse{at}math.univ-metz.fr We study the NeumannLaplacian eigenvalue problem in domainswith multiple cracks. We derive a mixed variational formulationwhich holds on the whole geometric domain (including the cracks)and implements efficient finite-element discretizations forthe computation of eigenvalues. Optimal error estimates aregiven and several numerical examples are presented, confirmingthe efficiency of the method. As applications, we numericallyinvestigate the behaviour of the low eigenvalues in domainswith a large number of cracks. |
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Keywords: | eigenvalues Neumann Laplacian domains with cracks finite elements method |
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