Free Access
Volume 45, Number 4, July-August 2011
Page(s) 697 - 738
Published online 10 December 2010
  1. 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. IMA J. Numer. Anal. 19 (1999) 147–168. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.W. Barrett and J.F. Blowey, Finite element approximation of an Allen-Cahn/Cahn-Hilliard system. IMA J. Numer. Anal. 22 (2002) 11–71. [CrossRef] [MathSciNet] [Google Scholar]
  3. 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]
  4. J.W. Barrett, J.F. Blowey and H. Garcke, On fully practical finite element approximations of degenerate Cahn-Hilliard systems. ESAIM: M2AN 35 (2001) 713–748. [CrossRef] [EDP Sciences] [Google Scholar]
  5. J.F. Blowey and C.M. Elliott, The Cahn-Hilliard gradient theory for phase separation with nonsmooth free energy. II. Numerical analysis. Eur. J. Appl. Math. 3 (1992) 147–179. [Google Scholar]
  6. J.F. Blowey, M.I.M. Copetti and C.M. Elliott, 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]
  7. F. Boyer, A theoretical and numerical model for the study of incompressible mixture flows. Comput. Fluids 31 (2002) 41–68. [CrossRef] [Google Scholar]
  8. F. Boyer and C. Lapuerta, Study of a three component Cahn-Hilliard flow model. ESAIM: M2AN 40 (2006) 653–687. [CrossRef] [EDP Sciences] [Google Scholar]
  9. F. Boyer, C. Lapuerta, S. Minjeaud and B. Piar, A local adaptive refinement method with multigrid preconditioning illustrated by multiphase flows simulations, in CANUM 2008, ESAIM Proc. 27, EDP Sciences, Les Ulis (2009) 15–53. [Google Scholar]
  10. F. Boyer, C. Lapuerta, S. Minjeaud, B. Piar and M. Quintard, Cahn-Hilliard/Navier-Stokes model for the simulation of three-phase flows. Transp. Porous Media 82 (2010) 463–483. [Google Scholar]
  11. K. Deimling, Nonlinear functional analysis. Springer-Verlag (1985). [Google Scholar]
  12. Q. Du and R.A. Nicolaides, Numerical analysis of a continuum model of phase transition. SIAM J. Numer. Anal. 28 (1991) 1310–1322. [CrossRef] [MathSciNet] [Google Scholar]
  13. C.M. Elliott, The Cahn-Hilliard model for the kinetics of phase separation, in Mathematical models for phase change problems, Óbidos, 1988, Internat. Ser. Numer. Math. 88, Birkhäuser, Basel (1989) 35–73. [Google Scholar]
  14. 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]
  15. C.M. Elliott and S. Luckhaus, A generalised diffusion equation for phase separation of a multi-component mixture with interfacial free energy. IMA Preprint Series # 887 (1991). [Google Scholar]
  16. C.M. Elliott and A.M. Stuart, The global dynamics of discrete semilinear parabolic equations. SIAM J. Numer. Anal. 30 (1993) 1622–1663. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Ern and J.-L. Guermond, Theory and Pratice of Finite Elements, Applied Mathematical Sciences 159. Springer (2004). [Google Scholar]
  18. D.J. Eyre, Unconditionally gradient stable time marching the Cahn-Hilliard equation, in Computational and mathematical models of microstructural evolution, San Francisco, CA, 1998, Mater. Res. Soc. Sympos. Proc. 529, MRS, Warrendale, PA (1998) 39–46. [Google Scholar]
  19. X. Feng, Fully discrete finite element approximations of the Navier-Stokes-Cahn-Hilliard diffuse interface model for two-phase fluid flows. SIAM J. Numer. Anal. 44 (2006) 1049–1072. [CrossRef] [MathSciNet] [Google Scholar]
  20. X. Feng, Y. He and C. Liu, Analysis of finite element approximations of a phase field model for two-phase fluids. Math. Comp. 76 (2007) 539–571. [CrossRef] [MathSciNet] [Google Scholar]
  21. H. Garcke and B. Stinner, Second order phase field asymptotics for multi-component systems. Interface Free Boundaries 8 (2006) 131–157. [Google Scholar]
  22. H. Garcke, B. Nestler and B. Stoth, A multiphase field concept: numerical simulations of moving phase boundaries and multiple junctions. SIAM J. Appl. Math. 60 (2000) 295–315. [Google Scholar]
  23. J. Kim and J. Lowengrub, Phase field modeling and simulation of three-phase flows. Interfaces Free Boundaries 7 (2005) 435–466. [Google Scholar]
  24. J. Kim, K. Kang and J. Lowengrub, Conservative multigrid methods for Cahn-Hilliard fluids. J. Comput. Phys. 193 (2004) 511–543. [CrossRef] [MathSciNet] [Google Scholar]
  25. J. Kim, K. Kang and J. Lowengrub, Conservative multigrid methods for ternary Cahn-Hilliard systems. Commun. Math. Sci. 2 (2004) 53–77. [MathSciNet] [Google Scholar]
  26. C. Lapuerta, Échanges de masse et de chaleur entre deux phases liquides stratifiées dans un écoulement à bulles. Mathématiques appliquées, Université de Provence, France (2006). [Google Scholar]
  27. H.G. Lee and J. Kim, A second-order accurate non-linear difference scheme for the n-component Cahn-Hilliard system. Physica A 387 (2008) 4787–4799. [CrossRef] [MathSciNet] [Google Scholar]
  28. B. Nestler, H. Garcke and B. Stinner, Multicomponent alloy solidification: Phase-field modeling and simulations. Phys. Rev. E 71 (2005) 041609. [CrossRef] [Google Scholar]
  29. PELICANS, Collaborative Development environment, [Google Scholar]
  30. J.S. Rowlinson and B. Widom, Molecular theory of capillarity. Clarendon Press (1982). [Google Scholar]
  31. J.M. Seiler and K. Froment, Material effects on multiphase phenomena in late phases of severe accidents of nuclear reactors. Multiph. Sci. Technol. 12 (2000) 117–257. [Google Scholar]
  32. J. Simon, Compact sets in the space Lp(0, T; B). Ann. Mat. Pura Appl. 146 (1987) 65–96. [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