Eigenvalue problems with sign-changing coefficients

Camille Carvalho; Lucas Chesnel; Patrick Ciarlet

doi:10.1016/j.crma.2017.05.002

Eigenvalue problems with sign-changing coefficients

Titre traduit de la contribution: Problèmes aux valeurs propres en présence de coefficients changeant de signe

Camille Carvalho
, Lucas Chesnel
, Patrick Ciarlet

University of California Merced
Université Paris-Saclay

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

11 Citations (Scopus)

Résumé

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.

Titre traduit de la contribution	Problèmes aux valeurs propres en présence de coefficients changeant de signe
langue originale	Anglais
Pages (de - à)	671-675
Nombre de pages	5
journal	Comptes Rendus Mathematique
Volume	355
Numéro de publication	6
Les DOIs	https://doi.org/10.1016/j.crma.2017.05.002
état	Publié - 1 juin 2017

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10.1016/j.crma.2017.05.002

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title = "Eigenvalue problems with sign-changing coefficients",

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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AB - 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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Eigenvalue problems with sign-changing coefficients

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