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FEM for elliptic eigenvalue problems: how coarse can the coarsest mesh be chosen? An experimental study

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Computing and Visualization in Science

Abstract

In this paper, we consider the numerical discretization of elliptic eigenvalue problems by Finite Element Methods and its solution by a multigrid method. From the general theory of finite element and multigrid methods, it is well known that the asymptotic convergence rates become visible only if the mesh width h is sufficiently small, h ≤ h 0. We investigate the dependence of the maximal mesh width h 0 on various problem parameters such as the size of the eigenvalue and its isolation distance. In a recent paper (Sauter in Finite elements for elliptic eigenvalue problems in the preasymptotic regime. Technical Report. Math. Inst., Univ. Zürich, 2007), the dependence of h 0 on these and other parameters has been investigated theoretically. The main focus of this paper is to perform systematic experimental studies to validate the sharpness of the theoretical estimates and to get more insights in the convergence of the eigenfunctions and -values in the preasymptotic regime.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Zürich, Winterthurerstr 190, 8057, Zurich, Switzerland

    L. Banjai & S. Sauter

  2. Institut für Informatik, Christian-Albrechts-Universität Kiel, Christian-Albrechts-Platz 4, 24118, Kiel, Germany

    S. Börm

Authors
  1. L. Banjai
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  2. S. Börm
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  3. S. Sauter
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Correspondence to S. Sauter.

Additional information

Communicated by G. Wittum.

Dedicated to Wolfgang Hackbusch on the occasion of his 60th birthday.

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Banjai, L., Börm, S. & Sauter, S. FEM for elliptic eigenvalue problems: how coarse can the coarsest mesh be chosen? An experimental study. Comput. Visual Sci. 11, 363–372 (2008). https://doi.org/10.1007/s00791-008-0101-5

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  • DOI: https://doi.org/10.1007/s00791-008-0101-5

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