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

Camille Carvalho
, Lucas Chesnel
, Patrick Ciarlet

University of California Merced
Université Paris-Saclay

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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.

Translated title of the contribution	Problèmes aux valeurs propres en présence de coefficients changeant de signe
Original language	English
Pages (from-to)	671-675
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	355
Issue number	6
DOIs	https://doi.org/10.1016/j.crma.2017.05.002
Publication status	Published - 1 Jun 2017

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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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AU - Ciarlet, Patrick

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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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DO - 10.1016/j.crma.2017.05.002

M3 - Article

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

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ER -

Eigenvalue problems with sign-changing coefficients

Abstract

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