Advertisement

Finite Difference Approximation of a Hyperbolic Transmission Problem

Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 42)

Abstract

In this paper we investigate an initial boundary value problem for a one-dimensional hyperbolic equation in two disjoint intervals. A finite difference scheme approximating this initial boundary value problem is proposed and analyzed. An estimate of the convergence rate is obtained.

Keywords

Weak Solution Difference Scheme Initial Boundary Finite Difference Scheme Disjoint Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

This research was supported by the Ministry of Science of the Republic of Serbia under project # 144005A.

References

  1. 1.
    Angelova, I.T., Vulkov, L.G.: High-order finite difference schemes for elliptic problems with intersecting interfaces. Appl. Math. Comput. 187, 824–843 (2007)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Caffarelli, L.: A monotonicity formula for heat functions in disjoint domains. In: Boundary-Value Problems for PDEs and Applications, RMA Res. Notes Appl. Math. 29, Masson, Paris, 53–60 (1993)Google Scholar
  3. 3.
    Datta, A.K.: Biological and bioenvironmental heat and mass transfer. Marcel Dekker, New York (2002)CrossRefGoogle Scholar
  4. 4.
    Givoli, D.: Exact representation on artificial interfaces and applications in mechanics. Appl. Mech. Rev. 52, 333–349 (1999)CrossRefGoogle Scholar
  5. 5.
    Givoli, D.: Finite element modeling of thin layers. Comput. Model. Eng. Sci. 5 (6), 497–514 (2004)Google Scholar
  6. 6.
    Jovanović, B.S., Vulkov, L.G.: Finite difference approximation of strong solutions of a parabolic interface problem on disconnected domains. Publ. Inst. Math. 83 (2008)Google Scholar
  7. 7.
    Jovanović, B.S., Vulkov, L.G.: Numerical solution of a hyperbolic transmission problem. Comput. Methods Appl. Math. 8, No 4 (2008)Google Scholar
  8. 8.
    Kandilarov, J., Vulkov, L.G.: The immersed interface method for two-dimensional heat-diffusion equations with singular own sources. Appl. Numer. Math. 57, 5–7, 486–497 (2007)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Koleva, M.: Finite element solution of boundary value problems with nonlocal jump conditions. Math. Model. Anal. 13, No 3, 383–400 (2008)Google Scholar
  10. 10.
    Lions, J.L., Magenes, E.: Non homogeneous boundary value problems and applications. Springer, Berlin and New York (1972)Google Scholar
  11. 11.
    Samarskiĭ, A.A.: Theory of difference schemes. Marcel Dekker, New York and Basel (2001)MATHCrossRefGoogle Scholar
  12. 12.
    Thomée, V.: Galerkin finite element methods for parabolic problems. Springer Series in Computational Mathematics Vol. 25, Springer, Berlin etc. (1997)Google Scholar
  13. 13.
    Vulkov, L.G.: Well posedness and a monotone iterative method for a nonlinear interface problem on disjoint intervals. Am. Inst. Phys., Proc. Ser. 946 (2007)Google Scholar
  14. 14.
    Wloka, J.: Partial differential equations. Cambridge University Press, Cambridge (1987)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of BelgradeBelgradeSerbia

Personalised recommendations