Local two-sided bounds for eigenvalues of self-adjoint operators

Gabriel Barrenechea, Lyonell Boulton, Nabile Boussaid

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3 Citations (Scopus)
35 Downloads (Pure)


We examine the equivalence between an extension of the Lehmann-Maehly-Goerisch method developed a few years ago by Zimmermann and Mertins, and a geometrically motivated method developed more recently by Davies and Plum. We establish a general framework which allows sharpening various previously known results in these two settings and determine explicit convergence estimates for both methods. We demonstrate the applicability of the method of Zimmermann and Mertins by means of numerical tests on the resonant cavity problem.
Original languageEnglish
Number of pages34
JournalNumerische Mathematik
Publication statusPublished - 18 Jun 2016


  • Eigenvalue enclosures
  • spectral pollution
  • finite element method
  • Maxwell equation


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