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Adaptive solution of elliptic PDE-eigenvalue problems. Part I: Eigenvalues

Please always quote using this URN:urn:nbn:de:0296-matheon-5650
  • We consider a new adaptive finite element (AFEM) algorithm for elliptic PDE-eigenvalue problems. In contrast to other approaches we incorporate the iterative solution of the resulting finite dimensional algebraic eigenvalue problems into the adaptation process. In this way we can balance the costs of the adaption process for the mesh with the costs for the iterative eigenvalue method. We present error estimates that incorporate the discretization errors, approximation errors in the eigenvalue solver and roundoff errors and use these for the adaptation process. We show that for the adaptation process it is possible to restrict to very few iterations of a Krylov subspace solver for the eigenvalue problem on coarse meshes. We present several examples and show that this new approach achieves much better complexity than previous AFEM approaches which assume that the algebraic eigenvalue problem is solved to full accuracy.

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Metadaten
Author:Volker Mehrmann, Agnieszka Miedlar
URN:urn:nbn:de:0296-matheon-5650
Referee:Reinhold Schneider
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/02/03
Release Date:2009/02/21
Tag:
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
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 / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N50 Mesh generation and refinement
Preprint Number:565
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