An Adaptive Finite Element Method with Asymptotic Saturation for Eigenvalue Problems

Please always quote using this URN: urn:nbn:de:0296-matheon-11924
  • This paper discusses adaptive finite element methods (AFEMs) for the solution of elliptic eigenvalue problems associated with partial differential operators. An adaptive method based on nodal-patch refinement leads to an asymptotic error reduction property for the computed sequence of simple eigenvalues and eigenfunctions. This justifies the use of the proven saturation property for a class of reliable and efficient hierarchical a posteriori error estimators. Numerical experiments confirm that the saturation property is present even for very coarse meshes for many examples; in other cases the smallness assumption on the initial mesh may be severe.

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Metadaten
Author:Carsten Carstensen, Joscha Gedicke, Volker Mehrmann, Agnieszka Miedlar
URN:urn:nbn:de:0296-matheon-11924
Referee:Dietmar Hömberg
Language:English
Date of first Publication:2012/12/17
Institute:Research Center Matheon
Humboldt-Universität zu Berlin
Technische Universität Berlin
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:993

$Rev: 13581 $