Free access
Issue
ESAIM: M2AN
Volume 43, Number 2, March-April 2009
Page(s) 239 - 275
DOI http://dx.doi.org/10.1051/m2an/2008052
Published online 07 February 2009
  1. P.M. Adler and J.-F. Thovert, Fractures and Fracture Networks. Kluwer Acad., Amsterdam (1999).
  2. B. Andreianov, F. Boyer and F. Hubert, Discrete duality finite volume schemes for Leray-Lions type elliptic problems on general 2D-meshes. Numer. Methods Partial Differential Equations 23 (2007) 145–195. [CrossRef] [MathSciNet]
  3. P. Angot, Finite volume methods for non smooth solution of diffusion models; application to imperfect contact problems, in Recent Advances in Numerical Methods and Applications, O.P. Iliev, M.S. Kaschiev, S.D. Margenov, B.H. Sendov and P.S. Vassilevski Eds., Proc. 4th Int. Conf. NMA'98, Sofia (Bulgarie), World Sci. Pub. (1999) 621–629.
  4. P. Angot, A model of fracture for elliptic problems with flux and solution jumps. C. R. Acad. Sci. Paris Ser. I Math. 337 (2003) 425–430.
  5. P. Angot, T. Gallouët and R. Herbin, Convergence of finite volume methods on general meshes for non smooth solution of elliptic problems with cracks, in Finite Volumes for Complex Applications II, R. Vilsmeier, F. Benkhaldoun and D. Hänel Eds., Hermès (1999) 215–222.
  6. J. Bear, C.-F. Tsang and G. de Marsily, Flow and Contaminant Transport in Fractured Rock. Academic Press, San Diego (1993).
  7. B. Berkowitz, Characterizing flow and transport in fractured geological media: A review. Adv. Water Resour. 25 (2002) 861–884. [CrossRef]
  8. C. Bernardi, M. Dauge and Y. Maday, Compatibilité de traces aux arêtes et coins d'un polyhèdre. C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 679–684.
  9. C. Bernardi, M. Dauge and Y. Maday, Polynomials in the Sobolev world. (2007) http://hal.archives-ouvertes.fr/hal-00153795.
  10. I.I. Bogdanov, V.V. Mourzenko, J.-F. Thovert and P.M. Adler, Effective permeability of fractured porous media in steady-state flow. Water Resour. Res. 107 (2002).
  11. F. Boyer and F. Hubert, Finite volume method for 2D linear and nonlinear elliptic problems with discontinuities. SIAM J. Numer. Anal. 46 (2008) 3032–3070. [CrossRef] [MathSciNet]
  12. Y. Caillabet, P. Fabrie, P. Landereau, B. Noetinger and M. Quintard, Implementation of a finite-volume method for the determination of effective parameters in fissured porous media. Numer. Methods Partial Differential Equations 6 (2000) 237–263. [CrossRef]
  13. Y. Caillabet, P. Fabrie, D. Lasseux and M. Quintard, Computation of large-scale parameters for dispersion in fissured porous medium using finite-volume method. Comput. Geosci. 5 (2001) 121–150. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  14. K. Domelevo and P. Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids. ESAIM: M2AN 39 (2005) 1203–1249. [CrossRef] [EDP Sciences]
  15. R. Eymard and T. Gallouët, H-convergence and numerical schemes for elliptic equations. SIAM J. Numer. Anal. 41 (2003) 539–562. [CrossRef] [MathSciNet]
  16. R. Eymard, T. Gallouët and R. Herbin, Finite Volume Methods, in Handbook of Numerical Analysis VII, P.G. Ciarlet and J.L. Lions Eds., North-Holland (2000) 713–1020.
  17. I. Faille, E. Flauraud, F. Nataf, S. Pégaz-Fiornet, F. Schneider and F. Willien, A new fault model in geological basin modelling. Application of finite volume scheme and domain decomposition methods, in Finite Volumes for Complex Applications III, R. Herbin and D. Kröner Eds., Hermes Penton Sci. (HPS) (2002) 543–550.
  18. B. Faybishenko, P.A. Witherspoon and S.M. Benson, Dynamics of Fluids in Fractured Rock, Geophysical Monograph Series 122. American Geophysical Union, Washington D.C. (2000).
  19. P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics 24. Pitman, Advanced Publishing Program, Boston (1985).
  20. F. Hermeline, Approximation of diffusion operators with discontinuous tensor coefficients on distorted meshes. Comput. Methods Appl. Mech. Engrg. 192 (2003) 1939–1959. [CrossRef] [MathSciNet]
  21. J. Jaffré, V. Martin and J.E. Roberts, Generalized cell-centered finite volume methods for flow in porous media with faults, in Finite Volumes for Complex Applications III, R. Herbin and D. Kröner Eds., Hermes Penton Sci. (HPS) (2002) 357–364.
  22. V. Martin, J. Jaffré and J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM J. Sci. Comput. 26 (2005) 1667–1691. [CrossRef] [MathSciNet]
  23. V. Mityushev and P.M. Adler, Darcy flow arround a two dimensional lense. Journal Phys. A: Math. Gen. 39 (2006) 3545–3560. [CrossRef]
  24. V. Reichenberger, H. Jakobs, P. Bastian and R. Helmig, A mixed-dimensional finite volume method for two-phase flow in fractured porous media. Adv. Water Resour. 29 (2006) 1020–1036. [CrossRef]

Recommended for you