Free Access
Volume 39, Number 4, July-August 2005
Page(s) 755 - 780
Published online 15 August 2005
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York, London (1975).
  2. P. Bénilan, M.G. Crandall and P. Sacks, Some L1 existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions. Appl. Math. Optim. 17 (1988) 203–224. [CrossRef] [MathSciNet]
  3. A.E. Berger, H. Brezis and J.C.W Rogers, A numerical method for solving the problem ut - Δƒ(u) = 0. RAIRO Anal. Numer. 13 (1979) 297–312. [MathSciNet]
  4. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer (1994).
  5. H. Brezis and A. Pazy, Convergence and approximation of semigroups of nonlinear operators in Banach spaces. J. Funct. Anal. 9 (1972) 63–74. [CrossRef] [MathSciNet]
  6. H. Brezis and W. Strauss, Semi-linear second-order elliptic equations in L1. J. Math. Soc. Japan 25 (1973) 565–590. [CrossRef] [MathSciNet]
  7. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North Holland, Amsterdam (1978).
  8. P.G. Ciarlet, Basic Error Estimates for Elliptic Problems, in Finite Element Methods (Part 1), P.G. Ciarlet and J.L. Lions Eds., Handbook of Numerical Analysis, 17–351, Elsevier Science Publishers B.V., Amsterdam (1991).
  9. P.G. Ciarlet and P.A. Raviart, Maximum principle and uniform convergence for the finite element method. Comput. Methods Appl. Mech. Engrg. 2 (1973) 17–31. [CrossRef] [MathSciNet]
  10. 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]
  11. B. Cockburn and G. Gripenberg, Continuous dependence on the nonlinearities of solutions of degenerate parabolic equations. J. Differential Equations 151 (1999) 231–251. [CrossRef] [MathSciNet]
  12. M.G. Crandall and T. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces. Amer. J. Math. 93 (1971) 265–293. [CrossRef] [MathSciNet]
  13. C.M. Elliott, Error analysis of the enthalpy method for the Stefan problem. IMA J. Numer. Anal. 7 (1987) 61–71. [CrossRef] [MathSciNet]
  14. C.M. Elliott and J.R. Ockendon, Weak and Variational Methods for Moving Boundary Problems. Pitman, Boston. Res. Notes Math. 59 (1982).
  15. A. Friedman, Variational Principles and Free-Boundary Problems. Wiley, New York (1982).
  16. H. Fujii, Some remarks on finite element analysis of time-dependent field problems, in Theory and Practice in Finite Element Structural Analysis, University of Tokyo Press, Tokyo (1973) 91–106.
  17. H. Fujita, N. Saito and T. Suzuki, Operator Theory and Numerical Methods. North-Holland, Amsterdam (2001).
  18. B.H. Gilding and L.A. Peletier, On a class of similarity solutions of the porous media equation. J. Math. Anal. Appl. 55 (1976) 351–364. [CrossRef] [MathSciNet]
  19. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985).
  20. W. Jäger and J. Kačur, Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes. RAIRO Modél. Math. Anal. Numér. 29 (1995) 605–627. [MathSciNet]
  21. J. Kačur, A. Handlovicová and M. Kacurová, Solution of nonlinear diffusion problems by linear approximation schemes. SIAM J. Numer. Anal. 30 1703-1722 (1993).
  22. T. Kato, Schrödinger operators with singular potentials. Israel J. Math. 13 (1972) 135–148. [CrossRef] [MathSciNet]
  23. M.N. Le Roux, Semi-discretization in time for a fast diffusion equation. J. Math. Anal. Appl. 137 (1989) 354–370. [CrossRef] [MathSciNet]
  24. M.N. Le Roux and P.E. Mainge, Numerical solution of a fast diffusion equation. Math. Comp. 68 (1999) 461–485. [CrossRef] [MathSciNet]
  25. P. Lesaint and J. Pousin, Error estimates for a nonlinear degenerate parabolic equation. Math. Comp. 59 (1992) 339–358. [CrossRef] [MathSciNet]
  26. E. Magenes, R.H. Nochetto and C. Verdi, Energy error estimates for a linear scheme to approximate nonlinear parabolic problems. RAIRO Modél. Math. Anal. Numér. 21 (1987) 655–678. [MathSciNet]
  27. E. Magenes, C. Verdi and A. Visintin, Semigroup approach to the Stefan problem with non-linear flux. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 75 (1983) 24–33.
  28. E. Magenes, C. Verdi, and A. Visintin, Theoretical and numerical results on the two-phase Stefan problem. SIAM J. Numer. Anal. 26 (1989) 1425–1438. [CrossRef] [MathSciNet]
  29. I. Miyadera, Nonlinear Semigroups. Amer. Math. Soc. Colloq. Publ. (1992).
  30. R.H. Nochetto, Error estimates for two-phase Stefan problems in several space variables. I. Linear boundary conditions. Calcolo 22 (1985) 457–499. [CrossRef] [MathSciNet]
  31. P.H. Nochetto, and C. Verdi, Approximation of degenerate parabolic problems using numerical integration. SIAM J. Numer. Anal. 25 (1988) 784–814. [CrossRef] [MathSciNet]
  32. L.A. Peletier, The porous media equation, in Applications of Nonlinear Analysis in the Physical Sciences (Bielefeld, 1979), Surveys Reference Works Math., 6, Pitman, Boston, Mass.-London (1981) 229–241.
  33. R. Rannacher and R. Scott, Some optimal error estimates for piecewise linear finite element approximation. Math. Comp. 38 (1982) 437–445. [CrossRef] [MathSciNet]
  34. M. Rose, Numerical methods for flows through porous media, I. Math. Comp. 40 (1983) 435–467. [CrossRef] [MathSciNet]
  35. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483–493. [CrossRef] [MathSciNet] [PubMed]
  36. R.E. White, An enthalpy formulation of the Stefan problem. SIAM J. Numer. Anal. 19 (1982) 1129–1157. [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