Free access
Issue
ESAIM: M2AN
Volume 38, Number 1, January-February 2004
Page(s) 129 - 142
DOI http://dx.doi.org/10.1051/m2an:2004006
Published online 15 February 2004
  1. S.M. Allen and J.W. Cahn, A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27 (1979) 1085–1095. [CrossRef]
  2. H. Brézis, Analyse fonctionnelle. Dunod, Paris (1999).
  3. G. Caginalp and X. Chen, Convergence of the phase-field model to its sharp interface limits. Euro. J. Appl. Math. 9 (1998) 417–445. [CrossRef]
  4. X. Chen, Spectrum for the Allen–Cahn, Cahn–Hilliard, and phase-field equations for generic interfaces. Comm. Partial Differantial Equations 19 (1994) 1371–1395. [CrossRef] [MathSciNet]
  5. Ph. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér 9 (1975) 77–84.
  6. R. Dautrey and J.-L. Lions, Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques. Masson (1988).
  7. P. de Mottoni and M. Schatzman, Geometrical evolution of developed interfaces. Trans. Amer. Math. Soc. 347 (1995) 1533–1589. [CrossRef] [MathSciNet]
  8. K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems iv: Nonlinear problems. SIAM J. Numer. Anal. 32 (1995) 1729–1749. [CrossRef] [MathSciNet]
  9. X. Feng and A. Prohl, Numerical analysis of the Allen–Cahn equation and approximation for mean curvature flows. Num. Math. 94 (2003) 33–65. [CrossRef] [MathSciNet]
  10. Ch. Makridakis and R.H. Nochetto, Elliptic reconstruction and a posteriori error estimates for parabolic problems. SIAM J. Numer. Anal. 41 (2003) 1585–1594. [CrossRef] [MathSciNet]
  11. J. Rappaz and J.-F. Scheid, Existence of solutions to a phase-field model for the solidification process of a binary alloy. Math. Methods Appl. Sci. 23 (2000) 491–513. [CrossRef] [MathSciNet]
  12. A. Schmidt and K. Siebert, ALBERT: An adaptive hierarchical finite element toolbox. Preprint 06/2000, Freiburg edition.

Recommended for you