Free Access
Issue
ESAIM: M2AN
Volume 21, Number 4, 1987
Page(s) 655 - 678
DOI https://doi.org/10.1051/m2an/1987210406551
Published online 31 January 2017
  1. Ph. BENILAN, Solutions intégrales d'équations d'évolution dans un espace de Banach, C. R. Acad. Sci. Paris, A-274 (1972), 47-50. [MR: 300164] [Zbl: 0246.47068]
  2. A. E. BERGER, H BREZIS &J. C. W. ROGERS, A numerical method for solving the problem $u_t-\Delta f(u)=0$ R.A.I.R.O. Anal. Numér., 13 (1979), 297-312. [EuDML: 193344] [MR: 555381] [Zbl: 0426.65052]
  3. A. BOSSAVIT,A. DAMLAMIAN & M. FREMOND Eds., Free boundary problems: applications and theory, vol. III, Research Notes in Math. 120, Pitman, Boston (1985). [MR: 863154] [Zbl: 0578.35003]
  4. H. BREZIS, On some degenerate non-linear parabolic equations, in Non-linear functional analysis (F. E. Browder Ed.), A.M.S. XVIII 1 (1970), 28-38. [MR: 273468] [Zbl: 0231.47034]
  5. H. BREZIS & A. PAZY, Convergence and approximation of semigroups of non-linear operators in Banach spaces, J. Funct. Anal., 9 (1972), 63-74. [MR: 293452] [Zbl: 0231.47036]
  6. 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. [MR: 391741] [Zbl: 0272.65101]
  7. M. G. CRANDALL&T. M. LIGGETT, Generation of semi-groups of non-linear transformations on general Banach spaces, Amer J. Math., 93 (1971), 265-298. [MR: 287357] [Zbl: 0226.47038]
  8. J. DOUGLAS Jr.& T. DUPONT, Galerkin methods for parabolic equations, SIAM J. Numer. Anal., 7 (1970), 575-626. [MR: 277126] [Zbl: 0224.35048]
  9. J. DOUGLAS Jr. & T. DUPONT, Alternating-direction Galerkin methods on rectangles, in Numerical solutions of partial differential equations, vol. II (B. Hubbard Ed.), Academic Press, New York (1971), 133-214. [MR: 273830] [Zbl: 0239.65088]
  10. J. DOUGLAS Jr., T. DUPONT & R. E. EWING, Incomplete iteration for time-stepping a Galerkin method for a quasilinear parabolic problem, SIAM J. Numer. Anal., 16 (1979), 503-522. [MR: 530483] [Zbl: 0411.65064]
  11. C. M. ELLIOTT, Error analysis of the enthalpy method for the Stefan problem, IMA J. Numer. Anal., 7 (1987), 61-71. [MR: 967835] [Zbl: 0638.65088]
  12. R. E. EWING, Efficient multistep procedures for nonlinear parabolic problems with nonlinear Neumann boundary conditions, Calcolo, 19 (1982), 231-252. [MR: 695388] [Zbl: 0522.65072]
  13. J. W. JEROME, Approximation of nonlinear evolution systems, Academic Press, New York (1983). [MR: 690582] [Zbl: 0512.35001]
  14. J. W. JEROME & M. E. ROSE, Error estimates for the multidimensional two-phase Stefan problem, Math. Comp., 39 (1982), 377-414. [MR: 669635] [Zbl: 0505.65060]
  15. J. L. LIONS & E. MAGENES, Non-homogeneous boundary value problems and applications, vol. I, Springer-Verlag, Berlin (1972). [MR: 350177] [Zbl: 0223.35039]
  16. M. LUSKIN, A Galerkin method for nonlinear parabolic equations with nonlinear boundary conditions, SIAM J. Numer. AnaL, 16 (1979), 284-299. [MR: 526490] [Zbl: 0405.65059]
  17. E. MAGENES, Problemi di Stefan bifase in piu variabili spaziali, V S.A.F.A., Catania, Le Matematiche, XXXVI (1981), 65-108. [Zbl: 0545.35096]
  18. E. MAGENES & C. VERDI, On the semigroup approach to the two-phase Stefan problem with nonlinear flux conditions, in [3], 28-39. [MR: 863159] [Zbl: 0593.35092]
  19. G. H. MEYER, Multidimensional Stefan problems, SIAM J. Numer. Anal., 10 (1973), 522-538. [MR: 331807] [Zbl: 0256.65054]
  20. R. H. NOCHETTO, Error estimates for two-phase Stefan problems in several space variables, I: linear boundary conditions, Calcolo, 22 (1985), 457-499. [MR: 859087] [Zbl: 0606.65084]
  21. R. H. NOCHETTO, Error estimates for two-phase Stefan problems in several space variables, II: nonlinear flux conditions, Calcolo, 22 (1985), 501-534. [MR: 859088] [Zbl: 0606.65085]
  22. R. H. NOCHETTO, Error estimates for multidimensional Stefan problems with general boundary conditions, in [3], 50-60. [MR: 863161] [Zbl: 0593.35094]
  23. R. H. NOCHETTO, Error estimates for multidimensional singular parabolic problems, Japan J. Appl. Math., 4 (1987), 111-138. [MR: 899207] [Zbl: 0657.65132]
  24. R. H. NOCHETTO& C. VERDI, Approximation of degenerate parabolic problems using numerical integration, SIAM J. Numer. Anal., to appear. [MR: 954786] [Zbl: 0655.65131]
  25. J. C. W. ROGERS, A. E. BERGER & M. CIMENT, The alternating phase truncation method for numerical solution of a Stefan problem, SIAM J. Numer. Anal., 16 (1979), 563-587. [MR: 537272] [Zbl: 0418.65051]
  26. M. E. ROSE, Numerical methods for flows through porous media I, Math. Comp., 40 (1983), 435-467. [MR: 689465] [Zbl: 0518.76078]
  27. V. THOMEE, Galerkin finite element methods for parabolic problems, Lecture Notes in Math. 1054, Springer-Verlag, Berlin (1984). [MR: 744045] [Zbl: 0528.65052]
  28. C. VERDI, On the numerical approach to a two-phase Stefan problem with nonlinear flux, Calcolo, 22 (1985), 351-381. [MR: 860658] [Zbl: 0612.65084]
  29. C. VERDI & A. VISINTIN, Error estimates for a semi-explicit numerical scheme for Stefan-type problems, submitted to Numer. Math. [EuDML: 133231] [MR: 923709] [Zbl: 0617.65125]
  30. A. VISINTIN, Stefan problem with phase relaxation, IMA J. Appl. Math., 34 (1985), 225-245. [MR: 804824] [Zbl: 0585.35053]
  31. M. F. WHEELER, A priori $L_2$-error estimates for Galerkin approximations to parabolic partial differential equations, SIAM J. Numer. Anal., 10 (1973), 723-759. [MR: 351124] [Zbl: 0232.35060]
  32. R. E. WHITE, An enthalpy formulation of the Stefan problem, SIAM J. Numer. Anal., 19 (1982), 1129-1157. [MR: 679656] [Zbl: 0501.65058]

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