Free access
Issue
ESAIM: M2AN
Volume 35, Number 4, July-August 2001
Page(s) 713 - 748
DOI http://dx.doi.org/10.1051/m2an:2001133
Published online 15 April 2002
  1. R.A. Adams and J. Fournier, Cone conditions and properties of Sobolev spaces. J. Math. Anal. Appl. 61 (1977) 713-734. [CrossRef] [MathSciNet]
  2. J.W. Barrett and J.F. Blowey, An error bound for the finite element approximation of a model for phase separation of a multi-component alloy. IMA J. Numer. Anal. 16 (1996) 257-287. [CrossRef] [MathSciNet]
  3. J.W. Barrett and J.F. Blowey, Finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy. Numer. Math. 77 (1997) 1-34. [CrossRef] [MathSciNet]
  4. J.W. Barrett and J.F. Blowey, Finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix. IMA J. Numer. Anal. 18 (1998) 287-328. [CrossRef] [MathSciNet]
  5. J.W. Barrett and J.F. Blowey, Finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy and a concentration dependent mobility matrix. M 3AS 9 (1999) 627-663.
  6. J.W. Barrett and J.F. Blowey, An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix. Numer. Math. 88 (2001) 255-297. [CrossRef] [MathSciNet]
  7. J.W. Barrett, J.F. Blowey and H. Garcke, Finite element approximation of a fourth order nonlinear degenerate parabolic equation. Numer. Math. 80 (1998) 525-556. [CrossRef] [MathSciNet]
  8. J.W. Barrett, J.F. Blowey and H. Garcke, Finite element approximation of the Cahn-Hilliard equation with degenerate mobility. SIAM J. Numer. Anal. 37 (1999) 286-318. [CrossRef] [MathSciNet]
  9. J.F. Blowey, M.I.M. Copetti and C.M. Elliott, The numerical analysis of a model for phase separation of a multi-component alloy. IMA J. Numer. Anal. 16 (1996) 111-139. [CrossRef] [MathSciNet]
  10. J.F. Blowey and C.M. Elliott, The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy, part i: Mathematical analysis. European J. Appl. Math. 2 (1991) 233-279. [CrossRef] [MathSciNet]
  11. J.F. Blowey and C.M. Elliott, The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy, part ii: Numerical analysis. European J. Appl. Math. 3 (1992) 147-179. [CrossRef] [MathSciNet]
  12. L. Bronsard, H. Garcke and B. Stoth, A multi-phase Mullins-Sekerka system: matched asymptotic expansions and an implicit time discretisation for the geometric evolution problem, in Proc. Roy. Soc. Edinburgh 128 A (1998) 481-506.
  13. J.F. Cialvaldini, Analyse numérique d'un problème de Stefan à deux phases par une méthode d'éléments finis. SIAM J. Numer. Anal. 12 (1975) 464-487. [CrossRef] [MathSciNet]
  14. P.G. Ciarlet, Introduction to numerical linear algebra and optimisation. C.U.P., Cambridge (1988).
  15. D. de Fontaine, An analysis of clustering and ordering in multicomponent solid solutions - I. Stability criteria. J. Phys. Chem. Solids 33 (1972) 297-310. [CrossRef]
  16. P.G. de Gennes, Dynamics of fluctuations and spinodal decomposition in polymer blends. J. Chem. Phys. 72 (1980) 4756-4763. [CrossRef] [MathSciNet]
  17. C.M. Elliott, The Cahn-Hilliard model for the kinetics of phase transitions, in Mathematical models for phase change problems, J.F. Rodrigues Ed., Internat. Ser. Numer. Math. 88, Birkhäuser-Verlag, Basel (1989) 35-73.
  18. C.M. Elliott and H. Garcke, On the Cahn-Hilliard equation with degenerate mobility. SIAM J. Math. Anal. 27 (1996) 404-423. [CrossRef] [MathSciNet]
  19. C.M. Elliott and H. Garcke, Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Physica D 109 (1997) 242-256. [CrossRef] [MathSciNet]
  20. C.M. Elliott and S. Luckhaus, A generalized diffusion equation for phase separation of a multi-component mixture with interfacial free energy. SFB256 University Bonn, Preprint 195 (1991).
  21. D.J. Eyre, Systems of Cahn-Hilliard equations. SIAM J. Appl. Math. 53 (1993) 1686-1712. [CrossRef] [MathSciNet]
  22. H. Garcke, B. Nestler and B. Stoth, Anisotropy in multi phase systems: a phase field approach. Interfaces Free Bound. 1 (1999) 175-198. [CrossRef] [MathSciNet]
  23. H. Garcke and A. Novick-Cohen, A singular limit for a system of degenerate Cahn-Hilliard equations. Adv. Diff. Eq. 5 (2000) 401-434.
  24. G. Grün and M. Rumpf, Nonnegativity preserving numerical schemes for the thin film equation. Numer. Math. 87 (2000) 113-152. [CrossRef] [MathSciNet]
  25. K. Ito and Y. Kohsaka, Three-phase boundary motion by surface diffusion: stability of a mirror symmetric stationary solution. Interfaces Free Bound. 3 (2001) 45-80. [CrossRef] [MathSciNet]
  26. P.L. Lions and B. Mercier, Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 16 (1979) 964-979. [CrossRef] [MathSciNet]
  27. J.E. Morral and J.W. Cahn, Spinodal decomposition in ternary systems. Acta Metall. 19 (1971) 1037-1045. [CrossRef]
  28. A. Novick-Cohen, The Cahn-Hilliard equation: mathematical and modelling perspectives. Adv. Math. Sci. Appl. 8 (1998) 965-985. [MathSciNet]
  29. F. Otto and W. E, Thermodynamically driven incompressible fluid mixtures. J. Chem. Phys. 107 (1997) 10177-10184. [CrossRef]
  30. L. Zhornitskaya and A.L. Bertozzi, Positivity preserving numerical schemes for lubrication-type equations. SIAM J. Numer. Anal. 37 (2000) 523-555. [CrossRef] [MathSciNet]

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