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.
Author: | Agnieszka Miedlar |
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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 |