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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board Member: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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Adaptive finite element solution of eigenvalue problems: Balancing of discretization and iteration error

R. Rannacher / A. Westenberger / W. Wollner

1*Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293/294, D-69120 Heidelberg, Germany

Citation Information: Journal of Numerical Mathematics. Volume 18, Issue 4, Pages 303–327, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: 10.1515/jnum.2010.015, December 2010

Publication History

Received:
2010-10-08
Published Online:
2010-12-20

Abstract

This paper develops a combined a posteriori analysis for the discretization and iteration errors in the solution of elliptic eigenvalue problems by the finite element method. The emphasis is on the iterative solution of the discretized eigenvalue problem by a Krylov-space method. The underlying theoretical framework is that of the Dual Weighted Residual (DWR) method for goal-oriented error estimation. On the basis of computable a posteriori error estimates the algebraic iteration can be adjusted to the discretization within a successive mesh adaptation process. The functionality of the proposed method is demonstrated by numerical examples.

Keywords:: eigenvalue problems; finite element method; mesh adaptation; DWR method; iteration error; stopping criteria

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