Finite Difference Scheme for a Parabolic Transmission Problem in Disjoint Domains

  • Zorica Milovanović
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)


In this paper we investigate a parabolic transmission problem in disjoint domains. A priori estimate for its weak solution in appropriate Sobolev-like space is proved. A finite difference scheme approximating this problem is proposed and analyzed.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amosov, A.A.: Global solvability of a nonlinear nonstationary problem with a nonlocal boundary condition of radiation heat transfer type. Differential Equations 41(1), 96–109 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Jovanović, B.S.: Finite difference method for boundary value problems with weak solutions. Posebna izdanja Mat. Instituta 16, Belgrade (1993)Google Scholar
  3. 3.
    Jovanović, B.S., Koleva, M.N., Vulkov, L.G.: Convergence of a FEM and two-grid algorithms for elliptic problems on disjoint domains. J. Comput. Appl. Math. 236, 364–374 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Jovanović, B.S., Vulkov, L.G.: Finite difference approximation of strong solutions of a parabolic interface problem on disconected domains. Publ. Inst. Math. 84(98), 37–48 (2008)CrossRefGoogle Scholar
  5. 5.
    Jovanović, B.S., Vulkov, L.G.: Numerical solution of a two-dimensional parabolic transmission problem. Int. J. Numer. Anal. Model. 7(1), 156–172 (2010)MathSciNetGoogle Scholar
  6. 6.
    Süli, E.: Finite element methods for partial differential equations. University of Oxford (2007)Google Scholar
  7. 7.
    Samarskii, A.A.: The theory of difference schemes. Marcel Dekker (2001)Google Scholar
  8. 8.
    Wloka, J.: Partial differential equations. Cambridge University Press (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Zorica Milovanović
    • 1
  1. 1.Faculty of MathematicsUniversity of BelgradeSerbia

Personalised recommendations