On the stability of the Rayleigh-Ritz method for eigenvalues

D. Gallistl, P. Huber, D. Peterseim

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7 Citations (Scopus)
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Abstract

This paper studies global stability properties of the Rayleigh–Ritz approximation of eigenvalues of the Laplace operator. The focus lies on the ratios λ^k/λk of the kth numerical eigenvalue λ^k and the kth exact eigenvalue λk . In the context of classical finite elements, the maximal ratio blows up with the polynomial degree. For B-splines of maximum smoothness, the ratios are uniformly bounded with respect to the degree except for a few instable numerical eigenvalues which are related to the presence of essential boundary conditions. These phenomena are linked to the inverse inequalities in the respective approximation spaces.
Original languageEnglish
Pages (from-to)339-351
Number of pages13
JournalNumerische Mathematik
Volume137
Issue number2
DOIs
Publication statusPublished - 2017
Externally publishedYes

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