Free access
Issue
ESAIM: M2AN
Volume 35, Number 4, July-August 2001
Page(s) 749 - 765
DOI http://dx.doi.org/10.1051/m2an:2001134
Published online 15 April 2002
  1. A. Friedman, The Stefan problem in several space variables. Trans. Amer. Math. Soc. 132 (1968) 51-87. [CrossRef]
  2. A.E. Berger, H. Brezis and J.C.W. Rogers, A numerical method for solving ut - Δƒ(u) = 0. RAIRO. Anal. Numér. 13 (1979) 297-312. [MathSciNet]
  3. C.M. Elliott, Error analysis of the enthalpy method for the Stefan problem. IMA J. Numer. Anal. 7 (1987) 61-71. [CrossRef] [MathSciNet]
  4. S.R. De Groot and P. Mazur, Non-equilibrium thermodynamics. North-Holland, Amsterdam (1962).
  5. H. Brezis, Analyse fonctionnelle, Théorie et applications. Masson, Paris (1993).
  6. H.W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations. Math. Z. 183 (1983) 311-341. [CrossRef] [MathSciNet]
  7. I. Prigogine, Thermodynamics of irreversible processes. Interscience Publ. (1967).
  8. J.D.P. Donnelly, A model for non-equilibrium thermodynamic processes involving phase changes. J. Inst. Math. Appl. 24 (1979) 425-438. [CrossRef] [MathSciNet]
  9. J.F. Ciavaldini, Analyse numérique d'un problème de Stefan à deux phases par une méthode d'éléments finis. SIAM J. Numer. Anal. 12 (1975) 464-487. [CrossRef] [MathSciNet]
  10. J.W. Jerome and M.E. Rose, Error estimates for the multidimensional two-phase Stefan problem. Math. Comp. 39 (1982) 377-414. [CrossRef] [MathSciNet]
  11. K. Yosida, Functional Analysis. Springer-Verlag, Berlin (1984).
  12. E. Magenes, Remarques sur l'approximation des problèmes paraboliques non-linéaires, in Analyse Mathématique et Applications, Gauthier-Villars, Paris (1988) 297-318.
  13. E. Magenes, R.H. Nochetto and C. Verdi, Energy error estimates for a linear scheme to approximate nonlinear parabolic problems. RAIRO. Modèl. Math. Anal. Numér. 21 (1987) 655-678. [MathSciNet]
  14. M. Crouzeix and A.L. Mignot, Analyse numérique des équations différentielles. Masson (1989).
  15. G.H. Meyer, Multidimensional Stefan problems. SIAM J. Numer. Anal. 10 (1973) 522-538. [CrossRef] [MathSciNet]
  16. O. Krüger, Modélisation et analyse numérique de problèmes de réaction-diffusion provenant de la solidification d'alliages binaires. Technical Report 2071, Thèse EPFL (1999).
  17. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985).
  18. M. Paolini, G. Sacchi and C. Verdi, Finite element approximations of singular parabolic problems. Internat. J. Numer. Methods Engrg. 26 (1988) 1989-2007. [CrossRef] [MathSciNet]
  19. P.G. Ciarlet, The Finite Element Method for Elliptic Problem. North Holland, Amsterdam (1978).
  20. J. Rulla, Error analysis for implicit approximations to Cauchy problems. SIAM J. Numer. Anal. 33 (1996) 68-87. [CrossRef] [MathSciNet]
  21. V. Thomée, Galerkin finite element methods for Parabolic Problems. Springer-Verlag, Berlin (1984).
  22. W. Jäger and J. Kačur, Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes. RAIRO. Modèl. Math. Anal. Numér. 29 (1995) 605-627. [MathSciNet]

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