Convergence analysis of adaptive finite element approximations of the Laplace eigenvalue problem

  • We consider an adaptive finite element method (AFEM) for the Laplace eigenvalue problem in bounded polygonal or polyhedral domains. We provide a convergence analysis based on a residual type a posteriori error estimator which consists of element and face residuals. The a posteriori error analysis further involves an oscillation term. We prove a reduction in the energy norm of the discretization error and the oscillation term. The proof of the reduction property uses the reliability and the discrete local efficiency of the estimator as well as a perturbed Galerkin orthogonality. Numerical results are given illustrating the performance of the AFEM.

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Metadaten
Author:Ronald H. W. HoppeGND, Haijun Wu, Zhimin Zhang
URN:urn:nbn:de:bvb:384-opus4-5055
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/637
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2008-12)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Contributing Corporation:University of Houston, Nanjing University, Wayne State University
Release Date:2008/03/13
Tag:adaptive finite element methods; convergence analysis; Laplace eigenvalue problem
GND-Keyword:Finite-Elemente-Methode; Konvergenz; Eigenwertproblem; A-posteriori-Abschätzung; Fehleranalyse
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik