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Optimal Order Finite Element Method for a Coupled Eigenvalue Problem on Overlapping Domains

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Large-Scale Scientific Computing (LSSC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4818))

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Abstract

The aim of this paper is to present a new finite element approach applied to a nonstandard second order elliptic eigenvalue problem, defined on two overlapping domains. We derive optimal error estimates as distinguished from [1], where they are suboptimal. For this purpose we introduce a suitable modified degrees of freedom and a corresponding interpolation operator. In order to fix the ideas and to avoid technical difficulties, we consider an one-dimensional case. The conclusive part presents numerical results.

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References

  1. De Shepper, H.: Finite element analysis of a coupling eigenvalue problem on overlapping domains. JCAM 132, 141–153 (2001)

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  5. Andreev, A.B., Dimov, T.T., Racheva, M.R.: One-dimensional patch-recovery finite element method for fourth-order elliptic problems. In: Li, Z., Vulkov, L.G., Waśniewski, J. (eds.) NAA 2004. LNCS, vol. 3401, pp. 108–115. Springer, Heidelberg (2005)

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Author information

Authors and Affiliations

  1. Department of Informatics, Technical University of Gabrovo, 5300, Gabrovo, Bulgaria

    A. B. Andreev

  2. Department of Mathematics, Technical University of Gabrovo, 5300, Gabrovo, Bulgaria

    M. R. Racheva

Authors
  1. A. B. Andreev
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  2. M. R. Racheva
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Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersen Plads, Building 321, DK-2800, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Andreev, A.B., Racheva, M.R. (2008). Optimal Order Finite Element Method for a Coupled Eigenvalue Problem on Overlapping Domains. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2007. Lecture Notes in Computer Science, vol 4818. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78827-0_73

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  • DOI: https://doi.org/10.1007/978-3-540-78827-0_73

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78825-6

  • Online ISBN: 978-3-540-78827-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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