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Eigenvalue problems with sign-changing coefficients

Camille Carvalho 1 Lucas Chesnel 2 Patrick Ciarlet 3
2 DeFI - Shape reconstruction and identification
Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We consider a class of eigenvalue problems involving coefficients changing sign on the domain of interest. We describe the main spectral properties of these problems according to the features of the coefficients. Then, under some assumptions on the mesh, we explain how one can use classical finite element methods to approximate the spectrum as well as the eigenfunctions while avoiding spurious modes. We also prove localisation results of the eigenfunctions for certain sets of coefficients.
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Submitted on : Tuesday, December 5, 2017 - 10:16:12 AM
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Camille Carvalho, Lucas Chesnel, Patrick Ciarlet. Eigenvalue problems with sign-changing coefficients. Comptes Rendus Mathématique, Elsevier Masson, 2017, 355 (6), pp.671 - 675. ⟨10.1016/j.crma.2017.05.002⟩. ⟨hal-01394856v2⟩

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