Eigenvalue problems with sign-changing coefficients - 13/06/17

Doi : 10.1016/j.crma.2017.05.002

Camille Carvalho ^a , Lucas Chesnel ^b , Patrick Ciarlet ^c
^a Applied Mathematics Unit, School of Natural Sciences, University of California, Merced, 5200 North Lake Road, Merced, CA 95343, USA
^b INRIA/Centre de mathématiques appliquées, École polytechnique, Université Paris-Saclay, route de Saclay, 91128 Palaiseau cedex, France
^c POEMS, UMR 7231 CNRS–INRIA–ENSTA, 828, boulevard des Maréchaux, 91762 Palaiseau cedex, France

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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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Résumé

Nous étudions, d'un point de vue théorique et numérique, des problèmes aux valeurs propres mettant en jeu des coefficients dont le signe change sur le domaine d'intérêt.

Il testo completo di questo articolo è disponibile in PDF.