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An Adaptive Finite Element Eigenvalue Solver of Quasi-Optimal Computational Complexity

Please always quote using this URN:urn:nbn:de:0296-matheon-6562
  • This paper presents a combined adaptive finite element method with an iterative algebraic eigenvalue solver for the Laplace eigenvalue problem of quasi-optimal computational complexity. The analysis is based on a direct approach for eigenvalue problems and allows the use of higher order conforming finite element spaces with fixed polynomial degree k>0. The optimal adaptive finite element eigenvalue solver (AFEMES) involves a proper termination criterion for the algebraic eigenvalue solver and does not need any coarsening. Numerical evidence illustrates the optimal computational complexity.

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Metadaten
Author:Carsten Carstensen, Joscha Gedicke
URN:urn:nbn:de:0296-matheon-6562
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/02/09
Release Date:2009/08/30
Tag:
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N15 Error bounds
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
Preprint Number:662
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