Skip to main content
SpringerLink
Log in

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

  • Conference paper
Numerical Analysis and Its Applications (NAA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5434))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Article  MathSciNet  Google Scholar 

  3. Huang, Y.Q., Xu, J.C.: A conforming finite element method for overlapping and nonmatching grids. Math. Comp. 72(243), 1057–1066 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  5. Raviart, P.A., Thomas, J.M.: Introduction a l’Analyse Numerique des Equations aux Derivees Partielles. Masson Paris (1983)

    Google Scholar 

  6. Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

Download references

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. R. Racheva
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

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

    Svetozar Margenov

  2. FNSE, Department of Numerical Methods and Statistics, University of Rousse, 8 Studentska str., 7017, Rousse, Bulgaria

    Lubin G. Vulkov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, 2800, Kongens, Lyngby, Denmark

    Jerzy Waśniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Andreev, A.B., Racheva, M.R. (2009). Optimal Order FEM for a Coupled Eigenvalue Problem on 2D Overlapping Domains. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00464-3_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00463-6

  • Online ISBN: 978-3-642-00464-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation