Free Access
Volume 38, Number 4, July-August 2004
Page(s) 633 - 652
Published online 15 August 2004
  1. J.W. Barrett and C.M. Elliott, A finite element method on a fixed mesh for the Stefan problem with convection in a saturated porous medium, in Numerical Methods for Fluid Dynamics, K.W. Morton and M.J. Baines Eds., Academic Press (London) (1982) 389–409.
  2. J.W. Barrett and R. Nürnberg, Convergence of a finite element approximation of surfactant spreading on a thin film in the presence of van der Waals forces. IMA J. Numer. Anal. 24 (2004) 323–363. [CrossRef] [MathSciNet]
  3. C.M. Elliott, On the finite element approximation of an elliptic variational inequality arising from an implicit time discretization of the Stefan problem. IMA J. Numer. Anal. 1 (1981) 115–125. [CrossRef] [MathSciNet]
  4. C.M. Elliott, Error analysis of the enthalpy method for the Stefan problem. IMA J. Numer. Anal. 7 (1987) 61–71. [CrossRef] [MathSciNet]
  5. C.M. Elliott and S. Larsson, A finite element model for the time-dependent Joule heating problem. Math. Comp. 64 (1995) 1433–1453. [CrossRef] [MathSciNet]
  6. R.F. Gariepy, M. Shillor and X. Xu, Existence of generalized weak solutions to a model for in situ vitrification. European J. Appl. Math. 9 (1998) 543–559. [CrossRef] [MathSciNet]
  7. S.S. Koegler and C.H. Kindle, Modeling of the in situ vitrification process. Amer. Ceram. Soc. Bull. 70 (1991) 832–835.
  8. J. Simon, Compact sets in the space Lp(0,T;B). Ann. Math. Pura. Appl. 146 (1987) 65–96.
  9. X. Xu, A compactness theorem and its application to a system of partial differential equations. Differential Integral Equations 9 (1996) 119–136. [MathSciNet]
  10. X. Xu, Existence for a model arising from the in situ vitrification process. J. Math. Anal. Appl. 271 (2002) 333–342. [CrossRef] [MathSciNet]

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