H. W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z, vol.183, issue.3, pp.311-341, 1983.

G. Amiez and P. Gremaud, On a numerical approach to Stefan-like problems, Numerische Mathematik, vol.26, issue.1, pp.71-89, 1991.
DOI : 10.1007/BF01385771

K. Amin and A. Khanna, CONVERGENCE OF AMERICAN OPTION VALUES FROM DISCRETE- TO CONTINUOUS-TIME FINANCIAL MODELS, Mathematical Finance, vol.2, issue.4, pp.289-304, 1994.
DOI : 10.1016/0304-405X(77)90021-6

J. Berton and R. Eymard, Finite volume methods for the valuation of American options, ESAIM: Mathematical Modelling and Numerical Analysis, vol.40, issue.2, pp.311-330, 2006.
DOI : 10.1051/m2an:2006011

M. Bertsch, P. De-mottoni, and L. A. Peletier, Degenerate diffusion and the Stefan problem, Nonlinear Analysis: Theory, Methods & Applications, vol.8, issue.11, pp.1311-1336, 1984.
DOI : 10.1016/0362-546X(84)90018-X

J. Carrillo, Entropy Solutions for Nonlinear Degenerate Problems, Archive for Rational Mechanics and Analysis, vol.147, issue.4, pp.269-361, 1999.
DOI : 10.1007/s002050050152

J. Droniou, R. Eymard, T. Gallouët, and R. Herbin, A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS, Mathematical Models and Methods in Applied Sciences, vol.20, issue.02, pp.265-295, 2010.
DOI : 10.1142/S0218202510004222

URL : https://hal.archives-ouvertes.fr/hal-00346077

J. Droniou, R. Eymard, T. Gallouët, and R. Herbin, GRADIENT SCHEMES: A GENERIC FRAMEWORK FOR THE DISCRETISATION OF LINEAR, NONLINEAR AND NONLOCAL ELLIPTIC AND PARABOLIC EQUATIONS, Mathematical Models and Methods in Applied Sciences, vol.23, issue.13, 2012.
DOI : 10.1142/S0218202513500358

URL : https://hal.archives-ouvertes.fr/hal-00751551

C. Elliott, Error Analysis of the Enthalpy Method for the Stefan Problem, IMA Journal of Numerical Analysis, vol.7, issue.1, pp.61-71, 1987.
DOI : 10.1093/imanum/7.1.61

R. Eymard, T. Gallouët, M. Ghilani, and R. Herbin, Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes, IMA Journal of Numerical Analysis, vol.18, issue.4, pp.563-594, 1998.
DOI : 10.1093/imanum/18.4.563

R. Eymard, T. Gallouët, R. Herbin, and A. Michel, Convergence of a finite volume scheme for nonlinear degenerate parabolic equations, Numerische Mathematik, vol.92, issue.1, pp.41-82, 2002.
DOI : 10.1007/s002110100342

R. Eymard, T. Gallouët, D. Hilhorst, and Y. N. Slimane, Finite volumes and nonlinear diffusion equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.32, issue.6, pp.747-761, 1998.
DOI : 10.1051/m2an/1998320607471

R. Eymard, C. Guichard, and R. Herbin, Small-stencil 3D schemes for diffusive flows in porous media, ESAIM: Mathematical Modelling and Numerical Analysis, vol.46, issue.2, pp.265-290, 2012.
DOI : 10.1051/m2an/2011040

URL : https://hal.archives-ouvertes.fr/hal-00542667

R. Eymard, R. Herbin, and A. Michel, Mathematical study of a petroleum-engineering scheme, ESAIM: Mathematical Modelling and Numerical Analysis, vol.37, issue.6, pp.937-972, 2003.
DOI : 10.1051/m2an:2003062

T. Gallouët and J. Latché, Compactness of discrete approximate solutions to parabolic PDEs - Application to a turbulence model, Communications on Pure and Applied Analysis, vol.11, issue.6, 2011.
DOI : 10.3934/cpaa.2012.11.2371

R. Nochetto and C. Verdi, Approximation of Degenerate Parabolic Problems Using Numerical Integration, SIAM Journal on Numerical Analysis, vol.25, issue.4, pp.784-814, 1988.
DOI : 10.1137/0725046