Finite volumes and nonlinear diffusion equations
Eymard, R. ; Gallouët, T. ; Hilhorst, D. ; Naït Slimane, Y.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 32 (1998), p. 747-761 / Harvested from Numdam
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@article{M2AN_1998__32_6_747_0,
     author = {Eymard, R. and Gallou\"et, T. and Hilhorst, D. and Na\"\i t Slimane, Y.},
     title = {Finite volumes and nonlinear diffusion equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {32},
     year = {1998},
     pages = {747-761},
     mrnumber = {1652593},
     zbl = {0914.65101},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1998__32_6_747_0}
}

Eymard, R.; Gallouët, T.; Hilhorst, D.; Naït Slimane, Y. Finite volumes and nonlinear diffusion equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 32 (1998) pp. 747-761. http://gdmltest.u-ga.fr/item/M2AN_1998__32_6_747_0/

[1] G. Amiez, P. A. Gremaud, On a numerical approach to Stefan-like problems, Numer. Math. 59, 71-89 (1991). | MR 1103754 | Zbl 0731.65107

[2] D. R. Atthey A Finite Difference Scheme for Melting Problems, J. Inst. Math. Appl. 13, 353-366 (1974). | MR 351295

[3] L. A. Baughman, N. J. Walkington, Co-volume methods for degenerate parabolic problems, Numer. Math. 64, 45-67 (1993). | MR 1191322 | Zbl 0797.65075

[4] A. E. Berger, H. Brezis, J. C. W. Rogers, A Numerical Method for Solving the Problem u1 - Δf(u) = 0, RAIRO Numerical Analysis, Vol. 13, 4, 297-312 (1979). | Numdam | MR 555381 | Zbl 0426.65052

[5] M. Bertsch, R. Kersner, L. A. Peletier, Positivity versus localization in degenerate diffusion equations, Nonlinear Analysis TMA, Vol. 9, 9, 987-1008 (1995). | MR 804564 | Zbl 0596.35073

[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, 464-488 (1975). IAM J. Numer. Anal., 12, 464-488 (1975). | MR 391741 | Zbl 0272.65101

[7] M. Guedda, D. Hilhorst, M. A. Peletier, Disappearing interfaces in nonlinear diffusion, to appear in Advances in Mathematical Sciences and Applications. | MR 1476273 | Zbl 0891.35071

[8] R. Herbin, An error estimate for a finite volume scheme for a diffusion convection problem on a triangular mesh, Num. Meth. P.D.E., 165-173 (1995). | MR 1316144 | Zbl 0822.65085

[9] S. L. Kamenomostskaja On the Stefan problem, Mat. Sb. 53(95), 489-514 (1961 in Russian). | MR 141895 | Zbl 0102.09301

[10] O. A. Ladyženskaja, V. A. Solonnikov, N. N. Ural'Ceva, Linear and Quasilinear Equations of Parabolic Type, Transl. of Math. Monographs, 23 (1968). | MR 241822 | Zbl 0174.15403

[11] A. M. Meirmanov, The Stefan Problem, Walter de Gruyter Ed., New York (1992). | MR 1154310 | Zbl 0751.35052

[12] G. H. Meyer, Multidimensional Stefan Problems, SIAM J. Num. Anal., 10, 522-538 (1973). | MR 331807 | Zbl 0256.65054

[13] R. H. Nochetto, Finite Element Methods for Parabolic Free Boundary Problems, Advances in Numerical Analysis, Vol. I: Nonlinear Partial Differential Equations and Dynamical Systems, W. Light ed., Oxford University Press, 34-88 (1991). | MR 1138471 | Zbl 0733.65089

[14] O. A. Oleinik, A method of solution of the general Stefan Problem, Sov. Math. Dokl. 1, 1350-1354 (1960). | MR 125341 | Zbl 0131.09202

[15] C. Verdi, Numerical aspects of parabolic free boundary and hysteresis problems, Phase Transitions and Hysteresis, A. Visinitin ed., Springer-Verlag, 213-284 (1994). | MR 1321834 | Zbl 0819.35155