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Optimal Order FEM for a Coupled Eigenvalue Problem on 2D Overlapping Domains

  • A. B. Andreev
  • M. R. Racheva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5434)

Abstract

In this paper we present a numerical approach to a nonstandard second-order elliptic eigenvalue problem defined on two overlapping rectangular domains with a nonlocal (integral) boundary condition. Usually, for this class of problems error estimates are suboptimal. By introducing suitable degrees of freedom and a corresponding interpolation operator we derive optimal order finite element approximation. Numerical results illustrate the efficiency of the proposed method.

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References

  1. 1.
    Andreev, A.B., Racheva, M.R.: Optimal order finite element method for coupled eigenvalue problem on overlappingdomains. In: Dimov, I.T., Lirkov, I., Margenov, S., Zlatev, Z. (eds.) NMA 2002. LNCS, vol. 2542, pp. 637–644. Springer, Heidelberg (2003)Google Scholar
  2. 2.
    De Shepper, H.: Finite element analysis of a coupling eigenvalue problem on overlapping domains. J. Comput. Appl. Math. 132, 141–153 (2001)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Huang, Y.Q., Xu, J.C.: A conforming finite element method for overlapping and nonmatching grids. Math. Comp. 72(243), 1057–1066 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cai, X.C., Dryja, M., Sarkis, M.: Overlapping nonmatchinggrids mortar element methods for elliptic problems. SIAM J. Numer. Anal. 36(2), 581–606 (1999)CrossRefzbMATHGoogle Scholar
  5. 5.
    Raviart, P.A., Thomas, J.M.: Introduction a l’Analyse Numerique des Equations aux Derivees Partielles. Masson Paris (1983)Google Scholar
  6. 6.
    Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978)zbMATHGoogle Scholar
  7. 7.
    Zienkiewich, O.C., Zhu, J.Z.: The superconvergence patch-recovery (SPR) and adaptive finite element refinement. Comp. Methods Appl. Mech. Eng. 101, 207–224 (1992)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • A. B. Andreev
    • 1
  • M. R. Racheva
    • 2
  1. 1.Department of InformaticsTechnical University of GabrovoGabrovoBulgaria
  2. 2.Department of MathematicsTechnical University of GabrovoGabrovoBulgaria

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