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Convergence of a Factorized Finite Difference Scheme for a Parabolic Transmission Problem

  • Zorica Milovanović JeknićEmail author
  • Boško Jovanović
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10187)

Abstract

In this paper, we consider a non-standard parabolic transmission problem in disjoint domains. A priori estimate for its weak solution in appropriate Sobolev-like space is proved. The convergence of a factorized finite difference scheme approximating this problem is analyzed.

Notes

Acknowledgement

The research of authors was supported by Ministry of Education, Science and Technological Development of Republic of Serbia under project 174015.

References

  1. 1.
    Amosov, A.A.: Global solvability of a nonlinear nonstationary problem with a nonlocal boundary condition of radiation heat transfer type. Differ. Equ. 41(1), 96–109 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bramble, J.H., Hilbert, S.R.: Bounds for a class of linear functionals with application to the Hermite interpolation. Numer. Math. 16, 362–369 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Jovanović, B.S.: Finite difference method for boundary value problems with weak solutions. Posebna izdanja Mat. Instituta 16, Belgrade (1993)Google Scholar
  4. 4.
    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
  5. 5.
    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)CrossRefzbMATHGoogle Scholar
  6. 6.
    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
  7. 7.
    Jovanović, B.S., Milovanović, Z.: Finite difference approximation of a parabolic problem with variable coefficients. Publ. Inst. Math. 95(109), 49–62 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Jovanović, B.S., Milovanović, Z.: Numerical approximation of 2D parabolic transmission problem in disjoint domains. Appl. Math. Comput. 228, 508–519 (2014)MathSciNetGoogle Scholar
  9. 9.
    Jovanović, B.S., Süli, E.: Analysis of Finite Difference Schemes. Springer Series in Computational Mathematics, vol. 46. Springer, Heidelberg (2013)zbMATHGoogle Scholar
  10. 10.
    Milovanović, Z.: Finite difference scheme for a parabolic transmission problem in disjoint domains. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) NAA 2012. LNCS, vol. 8236, pp. 403–410. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-41515-9_45 CrossRefGoogle Scholar
  11. 11.
    Samarskii, A.A.: The Theory of Difference Schemes. Marcel Dekker, New York (2001)CrossRefzbMATHGoogle Scholar
  12. 12.
    Samarskii, A.A., Lazarov, R.D., Makarov, V.L.: Difference Schemes for Differential Equations with Generalized Solutions. Vyshaya Shkola, Moscow (1987). (in Russian)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Zorica Milovanović Jeknić
    • 1
    Email author
  • Boško Jovanović
    • 2
  1. 1.Faculty of Construction ManagementUniversity “Union-Nikola Tesla”BelgradeSerbia
  2. 2.Faculty of MathematicsUniversity of BelgradeBelgradeSerbia

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