Free Access
Volume 37, Number 6, November-December 2003
Page(s) 937 - 972
Published online 15 November 2003
  1. H.W. Alt and E. DiBenedetto, Flow of oil and water through porous media. Astérisque 118 (1984) 89–108. Variational methods for equilibrium problems of fluids, Trento (1983).
  2. H.W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations. Math. Z. 183 (1983) 311–341. [CrossRef] [MathSciNet]
  3. S.N. Antontsev, A.V. Kazhikhov and V.N. Monakhov, Boundary value problems in mechanics of nonhomogeneous fluids. North-Holland Publishing Co., Amsterdam (1990). Translated from the Russian.
  4. T. Arbogast, M.F. Wheeler and N.-Y. Zhang, A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media. SIAM J. Numer. Anal. 33 (1996) 1669–1687. [CrossRef] [MathSciNet]
  5. K. Aziz and A. Settari, Petroleum reservoir simulation. Applied Science Publishers, London (1979).
  6. J. Bear, Dynamic of flow in porous media. Dover (1967).
  7. J. Bear, Modeling transport phenomena in porous media, in Environmental studies (Minneapolis, MN, 1992). Springer, New York (1996) 27–63.
  8. Y. Brenier and J. Jaffré, Upstream differencing for multiphase flow in reservoir simulation. SIAM J. Numer. Anal. 28 (1991) 685–696. [CrossRef] [MathSciNet]
  9. J. Carrillo, Entropy solutions for nonlinear degenerate problems. Arch. Rational. Mech. Anal. 147 (1999) 269–361. [CrossRef] [MathSciNet]
  10. G. Chavent and J. Jaffré, Mathematical models and finite elements for reservoir simulation. Elsevier (1986).
  11. Z. Chen, Degenerate two-phase incompressible flow. I. Existence, uniqueness and regularity of a weak solution. J. Differential Equations 171 (2001) 203–232. [CrossRef] [MathSciNet]
  12. Z. Chen, Degenerate two-phase incompressible flow. II. Regularity, stability and stabilization. J. Differential Equations 186 (2002) 345–376. [CrossRef] [MathSciNet]
  13. Z. Chen and R. Ewing, Mathematical analysis for reservoir models. SIAM J. Math. Anal. 30 (1999) 431–453. [CrossRef] [MathSciNet]
  14. Z. Chen and R.E. Ewing, Degenerate two-phase incompressible flow. III. Sharp error estimates. Numer. Math. 90 (2001) 215–240. [CrossRef] [MathSciNet]
  15. K. Deimling, Nonlinear functional analysis. Springer-Verlag, Berlin (1985).
  16. J. Droniou, A density result in sobolev spaces. J. Math. Pures Appl. 81 (2002) 697–714. [CrossRef] [MathSciNet]
  17. G. Enchéry, R. Eymard, R. Masson and S. Wolf, Mathematical and numerical study of an industrial scheme for two-phase flows in porous media under gravity. Comput. Methods Appl. Math. 2 (2002) 325–353. [MathSciNet]
  18. R.E. Ewing and R.F. Heinemann, Mixed finite element approximation of phase velocities in compositional reservoir simulation. R.E. Ewing Ed., Comput. Meth. Appl. Mech. Engrg. 47 (1984) 161–176. [CrossRef]
  19. R.E. Ewing and M.F. Wheeler, Galerkin methods for miscible displacement problems with point sources and sinks — unit mobility ratio case, in Mathematical methods in energy research (Laramie, WY, 1982/1983). SIAM, Philadelphia, PA (1984) 40–58.
  20. R. Eymard and T. Gallouët, Convergence d'un schéma de type éléments finis–volumes finis pour un système formé d'une équation elliptique et d'une équation hyperbolique. RAIRO Modél. Math. Anal. Numér. 27 (1993) 843–861. [MathSciNet]
  21. R. Eymard, T. Gallouët, M. Ghilani and R. Herbin, Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes. IMA J. Numer. Anal. 18 (1998) 563–594. [CrossRef] [MathSciNet]
  22. R. Eymard, T. Gallouët, R. Herbin and A. Michel, Convergence. Numer. Math. 92 (2002) 41–82. [CrossRef] [MathSciNet]
  23. R. Eymard, T. Gallouët, D. Hilhorst and Y. Naït Slimane, Finite volumes and nonlinear diffusion equations. RAIRO Modél. Math. Anal. Numér. 32 (1998) 747–761. [MathSciNet]
  24. R. Eymard, T. Gallouët and R. Herbin, Finite volume methods, in Handbook of numerical analysis, Vol. VII. North-Holland, Amsterdam (2000) 713–1020.
  25. R. Eymard, T. Gallouët and R. Herbin, Error estimate for approximate solutions of a nonlinear convection-diffusion problem. Adv. Differential Equations 7 (2002) 419–440. [MathSciNet]
  26. P. Fabrie and T. Gallouët, Modeling wells in porous media flow. Math. Models Methods Appl. Sci. 10 (2000) 673–709. [CrossRef] [MathSciNet]
  27. X. Feng, On existence and uniqueness results for a coupled system modeling miscible displacement in porous media. J. Math. Anal. Appl. 194 (1995) 883–910. [CrossRef] [MathSciNet]
  28. P.A. Forsyth, A control volume finite element method for local mesh refinements, in SPE Symposium on Reservoir Simulation. number SPE 18415, Texas: Society of Petroleum Engineers Richardson Ed., Houston, Texas (February 1989) 85–96.
  29. P.A. Forsyth, A control volume finite element approach to NAPL groundwater contamination. SIAM J. Sci. Statist. Comput. 12 (1991) 1029–1057. [CrossRef] [MathSciNet]
  30. Gérard Gagneux and Monique Madaune-Tort, Analyse mathématique de modèles non linéaires de l'ingénierie pétrolière. Springer-Verlag, Berlin (1996). With a preface by Charles-Michel Marle.
  31. R. Helmig, Multiphase Flow and Transport Processes in the Subsurface: A Contribution to the Modeling of Hydrosystems. Springer-Verlag Berlin Heidelberg (1997). P. Schuls (Translator).
  32. D. Kroener and S. Luckhaus, Flow of oil and water in a porous medium. J. Differential Equations 55 (1984) 276–288. [CrossRef] [MathSciNet]
  33. S.N. Kružkov and S.M. Sukorjanskiĭ, Boundary value problems for systems of equations of two-phase filtration type; formulation of problems, questions of solvability, justification of approximate methods. Mat. Sb. (N.S.) 104 (1977) 69–88, 175–176. [MathSciNet]
  34. A. Michel, A finite volume scheme for the simulation of two-phase incompressible flow in porous media. SIAM J. Numer. Anal. 41 (2003) 1301–1317. [CrossRef] [MathSciNet] [PubMed]
  35. A. Michel, Convergence de schémas volumes finis pour des problèmes de convection diffusion non linéaires. Ph.D. thesis, Université de Provence, France (2001).
  36. D.W. Peaceman, Fundamentals of Numerical Reservoir Simulation. Elsevier Scientific Publishing Co (1977).
  37. A. Pfertzel, Sur quelques schémas numériques pour la résolution des écoulements multiphasiques en milieu poreux. Ph.D. thesis, Universités Paris 6, France (1987).
  38. M.H. Vignal, Convergence of a finite volume scheme for an elliptic-hyperbolic system. RAIRO Modél. Math. Anal. Numér. 30 (1996) 841–872. [MathSciNet]
  39. H. Wang, R.E. Ewing and T.F. Russell, Eulerian-Lagrangian localized adjoint methods for convection-diffusion equations and their convergence analysis. IMA J. Numer. Anal. 15 (1995) 405–459. [CrossRef] [MathSciNet]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you