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Functional perturbation results and the balanced AFEM algorithm for self-adjoint PDE eigenvalue problems

Please always quote using this URN:urn:nbn:de:0296-matheon-8978
  • We introduce functional perturbation results for PDE eigenvalue problems including the functional backward error and the functional condition number. These results are used to establish a combined a posteriori error estimator embodying the discretization and the approximation error for the simple eigenpair. Based on known perturbation results in $H^{1}(\Omega)$ and $H^{-1}(\Omega)$ norms and a standard residual a posteriori error estimator, a balancing AFEM algorithm is proposed. The stopping criterion for the eigensolver is based on the equilibrating strategy, i.e., iterations proceed as long as the discrete part of the error estimator dominates the continuous part. All our statements are illustrated with several numerical examples.

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Metadaten
Author:Agnieszka Miedlar
URN:urn:nbn:de:0296-matheon-8978
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/09/09
Release Date:2011/09/09
Tag:
Institute:Research Center Matheon
Technische Universität Berlin
Project:C Energy and Materials (Production)
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N25 Eigenvalue problems
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems
Preprint Number:817
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