EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 35 / No 4 (July-August 2001) ESAIM: M2AN, 35 4 (2001) 713-748 References
Free Access
Issue
ESAIM: M2AN
Volume 35, Number 4, July-August 2001
Page(s) 713 - 748
DOI https://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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  14. P.G. Ciarlet, Introduction to numerical linear algebra and optimisation. C.U.P., Cambridge (1988). [Google Scholar]
  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] [Google Scholar]
  16. P.G. de Gennes, Dynamics of fluctuations and spinodal decomposition in polymer blends. J. Chem. Phys. 72 (1980) 4756-4763. [CrossRef] [MathSciNet] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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). [Google Scholar]
  21. D.J. Eyre, Systems of Cahn-Hilliard equations. SIAM J. Appl. Math. 53 (1993) 1686-1712. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  24. G. Grün and M. Rumpf, Nonnegativity preserving numerical schemes for the thin film equation. Numer. Math. 87 (2000) 113-152. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  27. J.E. Morral and J.W. Cahn, Spinodal decomposition in ternary systems. Acta Metall. 19 (1971) 1037-1045. [CrossRef] [Google Scholar]
  28. A. Novick-Cohen, The Cahn-Hilliard equation: mathematical and modelling perspectives. Adv. Math. Sci. Appl. 8 (1998) 965-985. [MathSciNet] [Google Scholar]
  29. F. Otto and W. E, Thermodynamically driven incompressible fluid mixtures. J. Chem. Phys. 107 (1997) 10177-10184. [CrossRef] [Google Scholar]
  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] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you