On spectral pollution

Finite difference and finite element approximations of eigenvalue problems, under certain circumstances, exhibit spectral pollution, i.e. the appearance of eigenvalues that do not converge to the correct value when the mesh density is increased. In the present paper this phenomenon is investigated i...

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Bibliographic Details
Published inComputer physics communications Vol. 59; no. 2; pp. 199 - 216
Main Authors Llobet, X., Appert, K., Bondeson, A., Vaclavik, J.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.06.1990
Elsevier Science
Subjects
Exact sciences and technology
Mathematical methods in physics
Numerical approximation and analysis
Physics
Finite element method
Eigenvalue problem
Dispersion relation
Mathematical operator
Finite difference method
Spectrum
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Summary:Finite difference and finite element approximations of eigenvalue problems, under certain circumstances, exhibit spectral pollution, i.e. the appearance of eigenvalues that do not converge to the correct value when the mesh density is increased. In the present paper this phenomenon is investigated in a homogeneous case by means of discrete dispersion relations: the polluting modes belong to a branch of the dispersion relation that is strongly distorted by the discretization method employed, or to a new, spurious branch. The analysis is applied to finite difference methods and to finite element methods, and some indications about how to avoid polluting schemes are given.
ISSN:0010-4655
1879-2944
DOI:10.1016/0010-4655(90)90170-6