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Numerical Treatment of Multiphase Flows in Porous Media pp 93–103Cite as

On the Discretization of Interface Problems with Perfect and Imperfect Contact

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Part of the book series: Lecture Notes in Physics ((LNP,volume 552))

Abstract

A second-order difference scheme for a first-order elliptic system with discontinuous coefficients is derived and studied. This approximation can be viewed as an improvement of the well-known scheme with harmonic averaging of the coefficients for a second order elliptic equation, which is first-order accurate for the gradient of the solution. The numerical experiments confirm the second order convergence for the scaled gradient, and demonstrate the advantages of the new discretization, compared with the older ones.

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References

  1. Angot, Ph., Modeling and visualization of thermal fields inside electronic systems under operating conditions, IBM Technical Report, TR-47095, 70 (1989).

    Google Scholar 

  2. Chernogorova, T. and Iliev, O., A 2nd order discretization of imperfect contact problems with piecewise constant coefficients on cell-centered grids, to appear in: Notes in Numerical Fluid Mechanics, M. Griebel et al (Eds), Proc. of Workshop on Large Scale Scientific Computations, June 1999, Sozopol, Bulgaria.

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  3. Ewing, R., Iliev, O., and Lazarov, R., A modified finite volume approximation of second order elliptic equations with discontinuous coefficients, TR ISC-99-01-MATH, Texas A&M University, 1999 (submitted).

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  4. Marchuk, G. I., Methods of computational mathematics, Moscow, Nauka, 1980.

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  5. Samarskii, A. A., Theory of difference schemes, Moscow, Nauka, 1977.

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  6. Samarskii, A. A. and Andréev, V. B., Finite difference methods for elliptic problems, Nauka Moscow, 1976 (in Russian), Méthodes aux Différences pour Équations Elliptiques, and MIR Moscou, 1978 (in French).

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  7. Wesseling, P., An Introduction to Multigrid Methods, Wiley, N.Y., 1991.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Informatics, The Sofia Univerity, St. Kl. Ohridski 5 J.Bouchier bul., BG-1163, Sofia, Bulgaria

    Tatiana Chernogorova

  2. Institute for Scientific Computation, Texas A&M University, College Station, Texas, 77843-3404, USA

    Richard E. Ewing

  3. Institute for Industrial Mathematics (ITWM), Erwin-Schroedinger str., bld. 49, D-67663, Kaiserslautern, Germany

    Oleg Iliev

  4. Department of Mathematics, Texas A&M University, College Station, Texas, 77843-3404, USA

    Raytcho Lazarov

Authors
  1. Tatiana Chernogorova
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  2. Richard E. Ewing
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  3. Oleg Iliev
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  4. Raytcho Lazarov
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Southern Methodist University, Box 750156, 75275-0156, Dallas, TX, USA

    Zhangxin Chen

  2. Institute for Scientific Computation, Texas A&M University, 77843-3404, College Station, TX, USA

    Richard E. Ewing

  3. Institute of ComputaTional Mathematics, Chinese Academy of Sciences, P.O.Box 2719, 100080, Beijing, P.R.China

    Zhong-Ci Shi

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© 2000 Springer-Verlag Berlin Heidelberg

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Cite this paper

Chernogorova, T., Ewing, R.E., Iliev, O., Lazarov, R. (2000). On the Discretization of Interface Problems with Perfect and Imperfect Contact. In: Chen, Z., Ewing, R.E., Shi, ZC. (eds) Numerical Treatment of Multiphase Flows in Porous Media. Lecture Notes in Physics, vol 552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45467-5_7

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  • DOI: https://doi.org/10.1007/3-540-45467-5_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67566-2

  • Online ISBN: 978-3-540-45467-0

  • eBook Packages: Springer Book Archive

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