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A Posteriori Error estimators for Non-Symmetric Eigenvalue Problems

Please always quote using this URN:urn:nbn:de:0296-matheon-6535
  • A posteriori error estimators for non-symmetric eigenvalue model problems are discussed in [Heuveline and Rannacher, A posteriori error control for finite element approximations of elliptic eigenvalue problems, 2001] in the context of the dual-weighted residual method (DWR). This paper directly analyses the variational formulation rather than the non-linear ansatz of Becker and Rannacher for some convection-diffusion model problem and presents error estimators for the eigenvalue error based on averaging techniques. In the case of linear P1 finite elements and globally constant coefficients, the error estimates of the residual and averaging error estimators are refined. Moreover, several postprocessing techniques attached to the DWR paradigm plus two new dual-weighted error estimators are compared in numerical experiments. The first new estimator utilises an auxiliary Raviart-Thomas mixed finite element method and the second exploits an averaging technique in combination with ideas of DWR.

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Metadaten
Author:Joscha Gedicke, Carsten Carstensen
URN:urn:nbn:de:0296-matheon-6535
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/08/08
Release Date:2009/07/08
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:659
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