Free Access
Issue
ESAIM: M2AN
Volume 43, Number 3, May-June 2009
Page(s) 563 - 589
DOI https://doi.org/10.1051/m2an/2009011
Published online 30 April 2009
  1. J.L. Boldrini and G. Planas, Weak solutions of a phase-field model for phase change of an alloy with thermal properties. Math. Methods Appl. Sci. 25 (2002) 1177–1193. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.L. Boldrini and C. Vaz, A semidiscretization scheme for a phase-field type model for solidification. Port. Math. (N.S.) 63 (2006) 261–292. [Google Scholar]
  3. S. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, Texts in Applied Mathathematics 15. Springer-Verlag, Berlin (1994). [Google Scholar]
  4. E. Burman, D. Kessler and J. Rappaz, Convergence of the finite element method applied to an anisotropic phase-field model. Ann. Math. Blaise Pascal 11 (2004) 67–94. [MathSciNet] [Google Scholar]
  5. G. Caginalp and W. Xie, Phase-field and sharp-interface alloy models. Phys. Rev. E 48 (1993) 1897–1909. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Ern and J.L.Guermond, Theory and practice of finite elements, Applied Mathematical Sciences 159. Springer, New York (2004). [Google Scholar]
  7. X. Feng and A. Prohl, Analysis of a fully discrete finite element method for the phase field model and approximation of its sharp interface limits. Math. Comp. 73 (2004) 541–567. [CrossRef] [MathSciNet] [Google Scholar]
  8. F. Guillén-González and J.V. Gutiérrez-Santacreu, Unconditional stability and convergence of a fully discrete scheme for 2D viscous fluids models with mass diffusion. Math. Comp. 77 (2008) 1495–1524 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  9. O. Kavian, Introduction à la Théorie des Points Critiques, Mathématiques et Applications 13. Springer, Berlin (1993). [Google Scholar]
  10. D. Kessler and J.F. Scheid, A priori error estimates of a finite-element method for an isothermal phase-field model related to the solidification process of a binary alloy. IMA J. Numer. Anal. 22 (2002) 281–305. [CrossRef] [MathSciNet] [Google Scholar]
  11. R. Rannacher and R. Scott, Some optimal error estimates for piecewise linear finite element approximations. Math. Comp. 38 (1982) 437–445. [CrossRef] [MathSciNet] [Google Scholar]
  12. J.F. Scheid, Global solutions to a degenerate solutal phase field model for the solidification of a binary alloy. Nonlinear Anal. 5 (2004) 207–217. [CrossRef] [MathSciNet] [Google Scholar]
  13. J. Simon, Compact sets in the Space Lp(0,T;B). Ann. Mat. Pura Appl. 146 (1987) 65–97. [Google Scholar]

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