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Construction and Convergence of Difference Schemes for a Modell Elliptic Equation with Dirac-delta Function Coefficient

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Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

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Abstract

We first discuss the difficulties that arise at the construction of difference schemes on uniform meshes for a specific elliptic interface problem. Estimates for the rate of convergence in discrete energetic Sobolev’s norms compatible with the smoothness of the solution are also presented.

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References

  1. Li Z.: The Immersed Interface Method-A Numerical Approach for Partial Differential Equations with Interfaces. PhD thesis, University of Washington, 1994.

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  2. Wiegmann A., Bube K.: The immersed interface method for nonlinear differential equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 35 (1998), 177–200.

    Article  MATH  MathSciNet  Google Scholar 

  3. Beyer R. P., Leveque R. J.: Analysis of one-dimensional model for the immersed boundary method, SIAM J. Numer. Anal. 29 (1992), 332-364.

    Google Scholar 

  4. Kandilarov J.: A second-order difference method for solution of diffusion problems with localized chemical reactions. in Finite-Difference methods: Theory and Applications (CFDM 98), Vol. 2, 63–67, Ed. by A. A. Samarskii, P. P. Matus, P. N. Vabishchevich, Inst. of Math., Nat. Acad. of Sci. of Belarus, Minsk 1998.

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  5. Vulkov L., Kandilarov J.: Construction and implementation of finite-difference schemes for systems of diffusion equations with localized chemical reactions, Comp. Math. and Math. Phys., 40, N 5, (2000), 705–717.

    MATH  Google Scholar 

  6. Samarskii A. A.: Theory of difference schemes, Nauka, Moscow 1987 (in Russian).

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  7. Samarskii A. A., Lazarov R. D., Makarov V. L.: Difference schemes for differential equations with generalized solutions, Vyshaya Shkola, Moscow 1989 (in Russian).

    Google Scholar 

  8. Jovanović B. S.: Finite difference method for boundary value problems with weak solutions, Mat. Institut, Belgrade 1993.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000, Belgrade, Yugoslavia

    B. S. Jovanović

  2. Department of Applied Mathematics and Informatics, University of Rousse, Studentska str. 8, 7017, Rousse, Bulgaria

    J. D. Kandilarov & L. G. Vulkov

Authors
  1. B. S. Jovanović
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  2. J. D. Kandilarov
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  3. L. G. Vulkov
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rousse, 7000, Rousse, Bulgaria

    Lubin Vulkov  & Plamen Yalamov  & 

  2. UNI-C,Danish Computing Center for Research and Education, DTU,Building 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2001 Springer-Verlag Berlin Heidelberg

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Jovanović, B.S., Kandilarov, J.D., Vulkov, L.G. (2001). Construction and Convergence of Difference Schemes for a Modell Elliptic Equation with Dirac-delta Function Coefficient. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_50

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  • DOI: https://doi.org/10.1007/3-540-45262-1_50

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

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