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A posteriori estimates for eigenvalue/vector approximations
Author(s) -
Grubišić Luka
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610016
Subject(s) - eigenvalues and eigenvectors , estimator , finite element method , a priori and a posteriori , mathematics , mathematical analysis , statistics , physics , philosophy , thermodynamics , epistemology , quantum mechanics
We combine abstract eigenvalue/eigenvector estimates (from our earlier work) with a saturation assumption for finite element solution of associated stationary problem to obtain a posteriori estimates of the accuracy of finite element Rayleigh–Ritz approximations. Attention will be payed to the interplay between the accuracy estimate for the finite element method and a strategy for generating an adapted mesh. The obtained results use a preconditioned residuum of Neymeyr and extend his study of eigenvalue approximations with eigenvector estimates. We also prove that this eigenvalue estimator is equivalent to the global error. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)