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New Approach of FEM for Eigenvalue Problems with Non-local Transition Conditions

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

Abstract

This paper is considered with the finite element method (FEM) for second order eigenvalue problems on a bounded multi-compo- nent domain in the plane. Non-local transition conditions on the interfaces between any two adjacent subdomains are imposed. A new finite element approach is proposed based on much more comprehensible theoretical proofs obtained under lower regularity requirements. The utility of this strategy when superconvergent postprocessing procedure is used as well as the numerical implementation are discussed. Finally, some numerical results are given.

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References

  1. 1.
    De Shepper, H., Van Keer, R.: A finite element method for elliptic eigenvalue problems in a multi-component domain in 2D with non-local Dirichlet transition conditions. J. Comput. Appl. Math. 111, 253–265 (1999)MathSciNetCrossRefGoogle Scholar
  2. 2.
    De Shepper, H., Van Keer, R.: On a variational approximation method for 2nd order eigenvalue problems in a multi-component domain with nonlocal Dirichlet transition conditions. Numer. Func. Anal. Optim. 19(9&10), 971–994 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Andreev, A.B., Racheva, M.R.: Optimal order FEM for a coupled eigenvalue problem on 2D overlapping domains. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds.) NAA 2008. LNCS. vol. 5434, Springer, Heidelberg (2008)Google Scholar
  4. 4.
    Andreev, A.B., Racheva, M.R.: Superconvergence of the interpolated quadratic finite elements on triangular meshes. Math. Balkanica, New Series 19, 3-4, 385–404 (2005)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Lin, Q., Yan, N., Zhou, A.: A rectangular test for interpolated finite elements. In: Proceedings of Systems Science & Systems Engineering, pp. 217–229. Culture Publish Co. (1991)Google Scholar
  6. 6.
    Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978)zbMATHGoogle 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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