Spectral pollution and eigenvalue bounds

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Abstract

The Galerkin method can fail dramatically when applied to eigenvalues in gaps of the extended essential spectrum. This phenomenon, called spectral pollution, is notoriously difficult to predict and it can occur in models from relativistic quantum mechanics, solid state physics, magnetohydrodynamics and elasticity theory. The purpose of this survey paper is two-fold. On the one hand, it describes a rigorous mathematical framework for spectral pollution. On the other hand, it gives an account on two complementary state-of-the-art Galerkin-type methods for eigenvalue computation which prevent spectral pollution completely.

Original languageEnglish
Article number2964
Pages (from-to)1-23
Number of pages23
JournalApplied Numerical Mathematics
Volume99
Early online date9 Sep 2015
DOIs
Publication statusPublished - Jan 2016

Keywords

  • Galerkin method
  • Numerical estimation of eigenvalue bounds
  • Projection methods
  • Second order spectrum
  • Spectral pollution
  • Spurious eigenvalues

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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