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Domain Decomposition for Some Transmission Problems in Flow in Porous Media

  • Clarisse Alboin
  • Jérôme Jaffré
  • Jean E. Roberts
  • Xuewen Wang
  • Christophe Serres
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 552)

Abstract

A variety of models are considered: one-phase flow in a porous medium, two-phase flow in a porous medium with two rock types, and one-phase flow in a porous medium with fractures. For each of these models the domain of calculation is divided into subdomains corresponding to the physics of the problem. Then it is shown how to rewrite the problems as interface problems to use nonoverlapping domain decomposition.

Keywords

porous media flow domain decomposition 

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References

  1. [1]
    Brezzi, F. and Fortin, M., Mixed and Hybrid Finite Element Methods, Springer Verlag, Berlin, 1991.zbMATHGoogle Scholar
  2. [2]
    Chavent, G. and Jaffré, J., Mathematical Models and Finite Elements for Reservoir Simulation, volume 17 of Studies in Mathematics and its Applications. North Holland, Amsterdam, Amsterdam, 1986.Google Scholar
  3. [3]
    Cowsar, L., Mandel, J., and Wheeler, M., Balancing domain decomposition for mixed finite elements, Math. of Comp. 64 (1993), 989–1015.CrossRefADSMathSciNetGoogle Scholar
  4. [4]
    Douglas, J., Jr. and Dupont, T., Galerkin methods for parabolic equations, SINUM 7 (1970), 575–626.MathSciNetzbMATHGoogle Scholar
  5. [5]
    Glowinski, R. and Wheeler, M., Domain decomposition and mixed finite element methods for elliptic problems, in Glowinski, R. et al., editor, Proceedings of the First Symposium on Domain Decomposition Methods for PDEs, SIAM, Philadelphia, 1987, 144–172.Google Scholar
  6. [6]
    Le Tallec, P., De Roeck, Y.-H., and Vidrascu, M., Domain decomposition methods for large linearly elliptic three dimensional problems, J. Comp. Appl. Math. 34 (1991). 341–362.CrossRefGoogle Scholar
  7. [7]
    Mandel, J., Balancing domain decomposition, Comm. in Numerical Methods in Engineering 9 (1993), 233–241.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Raviart, P.-A. and Thomas, J.-M., A mixed finite element method method for second order elliptic problems, in I. Galligani and E. Magenes, editors, Mathematical Aspects of Finite Element Methods; Lecture Notes in Mathematics 606, Springer, Berlin, 1977, 292–315.CrossRefGoogle Scholar
  9. [9]
    Roberts, J. E. and Thomas, J.-M., Mixed and hybrid methods, in P.G. Ciarlet and J.L. Lions, editors, Handbook of Numerical Analysis Vol.II, North Holland, Amsterdam, 1991, 523–639.Google Scholar
  10. [10]
    Smith, B., Bjorstadt, P., and Gropp, W., Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Clarisse Alboin
    • 1
  • Jérôme Jaffré
    • 1
  • Jean E. Roberts
    • 1
  • Xuewen Wang
    • 1
  • Christophe Serres
    • 2
  1. 1.INRIA-Rocquencourt, BP 105CedexFrance
  2. 2.IPSN/DES/SESID, BP 6Fontenay Aux Roses CedexFrance

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