Free Access
Issue
ESAIM: M2AN
Volume 37, Number 3, May-June 2003
Page(s) 417 - 431
DOI https://doi.org/10.1051/m2an:2003035
Published online 15 April 2004
  1. H.W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations. Math. Z. 183 (1983) 311–341. [CrossRef] [MathSciNet] [Google Scholar]
  2. H.W. Alt, S. Luckhaus and A. Visintin, On the nonstationary flow through porous media. Ann. Math. Pura Appl. CXXXVI (1984) 303–316. [Google Scholar]
  3. J. Babušikova, Application of relaxation scheme to degenerate variational inequalities. Appl. Math. 46 (2001) 419–439. [CrossRef] [MathSciNet] [Google Scholar]
  4. J.W. Barrett and P. Knabner, Finite element approximation of transport of reactive solutes in porous media. II: Error estimates for equilibrium adsorption processes. SIAM J. Numer. Anal. 34 (1997) 455–479. [CrossRef] [MathSciNet] [Google Scholar]
  5. J.W. Barrett and P. Knabner, An improved error bound for a Lagrange-Galerkin method for contaminant transport with non-lipschitzian adsorption kinetics. SIAM J. Numer. Anal. 35 (1998) 1862–1882. [CrossRef] [MathSciNet] [Google Scholar]
  6. J. Bear, Dynamics of Fluid in Porous Media. Elsevier, New York (1972). [Google Scholar]
  7. R. Bermejo, Analysis of an algorithm for the Galerkin-characteristics method. Numer. Math. 60 (1991) 163–194. [CrossRef] [MathSciNet] [Google Scholar]
  8. R. Bermejo, A Galerkin-characteristics algorithm for transport-diffusion equation. SIAM J. Numer. Anal. 32 (1995) 425–455. [CrossRef] [MathSciNet] [Google Scholar]
  9. C.N. Dawson, C.J. Van Duijn and M.F. Wheeler, Characteristic-Galerkin methods for contaminant transport with non-equilibrium adsorption kinetics. SIAM J. Numer. Anal. 31 (1994) 982–999. [CrossRef] [MathSciNet] [Google Scholar]
  10. R Douglas and T.F. Russel, Numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Numer. Anal. 19 (1982) 871–885. [CrossRef] [MathSciNet] [Google Scholar]
  11. R.E. Ewing and H. Wang, Eulerian-Lagrangian localized adjoint methods for linear advection or advection-reaction equations and their convergence analysis. Comput. Mech. 12 (1993) 97–121. [CrossRef] [MathSciNet] [Google Scholar]
  12. R. Eymard, M. Gutnic and D. Hilhorst, The finite volume method for Richards equation. Comput. Geosci. 3 (1999) 259–294. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  13. P. Frolkovic, Flux-based method of characteristics for contaminant transport in flowing groundwater. Computing and Visualization in Science 5 (2002) 73–83. [CrossRef] [MathSciNet] [Google Scholar]
  14. R. Glowinski, J.-L. Lions and R. Tremolieres, Numerical analysis of variational inequalities, Vol. 8. North-Holland Publishing Company, Stud. Math. Appl. (1981). [Google Scholar]
  15. A. Handlovicova, Solution of Stefan problems by fully discrete linear schemes. Acta Math. Univ. Comenianae (N.S.) 67 (1998) 351–372. [Google Scholar]
  16. H. Holden, K.H. Karlsen and K.-A. Lie, Operator splitting methods for degenerate convection-diffusion equations II: numerical examples with emphasis on reservoir simulation and sedimentation. Comput. Geosci. 4 (2000) 287–323. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  17. W. Jäger and J. Kačur, Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes. Math. Modelling Numer. Anal. 29 (1995) 605–627. [Google Scholar]
  18. J. Kačur, Solution of some free boundary problems by relaxation schemes. SIAM J. Numer. Anal. 36 (1999) 290–316. [CrossRef] [MathSciNet] [Google Scholar]
  19. J. Kačur, Solution to strongly nonlinear parabolic problems by a linear approximation scheme. IMA J. Numer. Anal. 19 (1999) 119–154. [CrossRef] [MathSciNet] [Google Scholar]
  20. J. Kačur, Solution of degenerate convection-diffusion problems by the method of characteristics. SIAM J. Numer. Anal. 39 (2001) 858–879. [CrossRef] [MathSciNet] [Google Scholar]
  21. J. Kačur and S. Luckhaus, Approximation of degenerate parabolic systems by nondegenerate alliptic and parabolic systems. Appl. Numer. Math. 25 (1997) 1–21. [CrossRef] [MathSciNet] [Google Scholar]
  22. J. Kačur and R. van Keer, Solution of contaminant transport with adsorption in porous media by the method of characteristics. ESAIM: M2AN 35 (2001) 981–1006. [CrossRef] [EDP Sciences] [Google Scholar]
  23. A. Kufner, O. John and S. Fučík, Function spaces. Academia, Prague (1977). [Google Scholar]
  24. J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Vol. XX. Dunod, Gauthier-Villars, Paris (1969). [Google Scholar]
  25. K. Mikula, Numerical solution of nonlinear diffusion with finite extinction phenomena. Acta Math. Univ. Comenian. (N.S.) 2 (1995) 223–292. [Google Scholar]
  26. J. Nečas, Les méthodes directes en théorie des équations elliptiques. Academia, Prague (1967). [Google Scholar]
  27. F. Otto, L1 – contraction and uniqueness for quasilinear elliptic – parabolic equations. C. R. Acad. Sci Paris Sér. I Math. 321 (1995) 105–110. [Google Scholar]
  28. P. Pironneau, On the transport-diffusion algorithm and its application to the Navier-Stokes equations. Numer. Math. 38 (1982) 309–332. [CrossRef] [Google Scholar]
  29. X. Shi, H. Wang and R.E. Ewing, An ellam scheme for multidimensional advection-reaction equations and its optimal-order error estimate. SIAM J. Numer. Anal. 38 (2001) 1846–1885. [CrossRef] [MathSciNet] [Google Scholar]

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