Free Access
Volume 17, Number 4, October-December 2011
Page(s) 931 - 954
Published online 18 August 2010
  1. R.A. Adams, Sobolev spaces, Pure and Applied Mathematics 65. Academic Press, New York-London (1975). [Google Scholar]
  2. L. Banas and R. Nürnberg, A multigrid method for the Cahn-Hilliard equation with obstacle potential. Appl. Math. Comput. 213 (2009) 290–303. [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, R. Nürnberg and V. Styles, Finite element approximation of a void electromigration model. SIAM J. Numer. Anal. 42 (2004) 738–772. [CrossRef] [MathSciNet] [Google Scholar]
  5. L. Blank, H. Garcke, L. Sarbu and V. Styles, Primal-dual active set methods for Allen-Cahn variational inequalities with non-local constraints. Preprint SPP1253-09-01 (2009). [Google Scholar]
  6. J.F. Blowey and C.M. Elliott, The Cahn-Hilliard gradient theory for phase separation with nonsmooth free energy. I. Mathematical analysis. Eur. J. Appl. Math. 2 (1991) 233–280. [CrossRef] [MathSciNet] [Google Scholar]
  7. 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]
  8. J.F. Blowey and C.M. Elliott, Curvature dependent phase boundary motion and parabolic double obstacle problems, in Degenerate Diffusions, W.-M. Ni, L.A. Peletier and J.L. Vazquez Eds., IMA Vol. Math. Appl. 47, Springer, New York (1993) 19–60. [Google Scholar]
  9. J.F. Blowey and C.M. Elliott, A phase field model with a double obstacle potential, in Motion by mean curvature, G. Buttazzo and A. Visintin Eds., de Gruyter (1994) 1–22. [Google Scholar]
  10. J.W. Cahn and J.E. Hilliard, Free energy of a nonuniform system. I. Interfacial energy. J. Chem. Phys. 28 (1958) 258–267. [CrossRef] [Google Scholar]
  11. I. Capuzzo Dolcetta, S.F. Vita and R. March, Area-preserving curve-shortening flows: From phase separation to image processing. Interfaces and Free Boundaries 4 (2002) 325–434. [CrossRef] [MathSciNet] [Google Scholar]
  12. X. Chen, Global asymptotic limit of solutions of the Cahn-Hilliard equation. J. Differential Geom. 44 (1996) 262–311. [MathSciNet] [Google Scholar]
  13. X. Chen, Z. Nashed and L. Qi, Smoothing methods and semismooth methods for nondifferentiable operator equations. SIAM J. Numer. Anal. 38 (2000) 1200–1216. [CrossRef] [MathSciNet] [Google Scholar]
  14. M. Copetti and C.M. Elliott, Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy. Numer. Math. 63 (1992) 39–65. [CrossRef] [MathSciNet] [Google Scholar]
  15. T.A. Davis, Algorithm 832: UMFPACK, an unsymmetric-pattern multifrontal method. ACM Trans. Math. Soft. 30 (2003) 196–199. [Google Scholar]
  16. T.A. Davis, A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. ACM Trans. Math. Soft. 34 (2003) 165–195. [Google Scholar]
  17. T.A. Davis and I.S. Duff, An unsymmetric-pattern multifrontal method for sparse LU factorization. SIAM J. Matrix Anal. Appl. 18 (1997) 140–158. [CrossRef] [MathSciNet] [Google Scholar]
  18. I.S. Duff and J.K. Reid, The multifrontal solution of indefinite sparse symmetric linear. ACM Trans. Math. Soft. 9 (1983) 302–325. [CrossRef] [Google Scholar]
  19. C.M. Elliott, The Cahn-Hilliard model for the kinetics of phase separation, in Mathematical models for phase change problems, Internat. Ser. Numer. Math. 88, Birkhäuser, Basel (1989). [Google Scholar]
  20. C.M. Elliott and A.R. Gardiner, One dimensional phase field computations, Numerical Analysis 1993, Proceedings of Dundee Conference, D.F. Griffiths and G.A. Watson Eds., Longman Scientific and Technical (1994) 56–74. [Google Scholar]
  21. C.M. Elliott and S. Luckhaus, A generalised diffusion equation for phase separation of a multi-component mixture with interfacial free energy. SFB 256, University of Bonn, Preprint 195 (1991). [Google Scholar]
  22. C.M. Elliott and J. Ockendon, Weak and Variational Methods for Moving Boundary Problems, Pitman Research Notes in Mathematics 59. Pitman (1982). [Google Scholar]
  23. L.C. Evans, Partial differential equations, Graduate Studies in Mathematics 19. American Mathematical Society, Providence (1998). [Google Scholar]
  24. A. Friedman, Variational principles and free-boundary problemsPure and Applied Mathematics. John Wiley & Sons, Inc., New York (1982). [Google Scholar]
  25. H. Garcke, Mechanical effects in the Cahn-Hilliard model: A review on mathematical results, in Mathematical Methods and Models in phase transitions, A. Miranvielle Ed., Nova Science Publ. (2005) 43–77. [Google Scholar]
  26. C. Gräser, Analysis und Approximation der Cahn-Hilliard Gleichung mit Hindernispotential. Diplomarbeit, Freie Universität Berlin, Fachbereich Mathematik und Informatik (2004). [Google Scholar]
  27. C. Gräser and R. Kornhuber, On preconditioned Uzawa-type iterations for a saddle point problem with inequality constraints, in Domain decomposition methods in science and engineering XVI, Lect. Notes Comput. Sci. Eng. 55, Springer, Berlin (2007) 91–102. [Google Scholar]
  28. C. Gräser and R. Kornhuber, Nonsmooth Newton methods for set-valued saddle point problems. SIAM J. Numer. Anal. 47 (2009) 1251–1273. [CrossRef] [MathSciNet] [Google Scholar]
  29. C. Gräser and R. Kornhuber, Multigrid methods for obstacle problems. J. Comput. Math. 27 (2009) 1–44. [MathSciNet] [Google Scholar]
  30. M. Hintermüller, K. Ito and K. Kunisch, The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13 (2002) 865–888. [Google Scholar]
  31. K. Ito and K. Kunisch, Semi-smooth Newton methods for variational inequalities of the first kind. ESAIM: M2AN 37 (2003) 41–62. [CrossRef] [EDP Sciences] [Google Scholar]
  32. B.M. Irons, A frontal solution scheme for finite element analysis. Int. J. Numer. Methods Eng. 2 (1970) 5–32. [CrossRef] [Google Scholar]
  33. D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications, Pure and Applied Mathematics 88. Academic Press, Inc., New York-London (1980). [Google Scholar]
  34. E. Kuhl and D.W. Schmid, Computational modeling of mineral unmixing and growth: An application of the Cahn-Hilliard equation. Comp. Mech. 39 (2007) 439–451. [CrossRef] [Google Scholar]
  35. 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]
  36. J.W.H. Liu, The multifrontal method for sparse matrix solution: Theory and practice. SIAM Rev. 34 (1992) 82–109. [Google Scholar]
  37. J. Lowengrub and L. Truskinovsky, Quasi-incompressible Cahn-Hilliard fluids and topological transitions. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 454 (1978) 2617–2654. [Google Scholar]
  38. A. Novick-Cohen, The Cahn-Hilliard equation: mathematical and modeling perspectives. Adv. Math. Sci. Appl. 8 (1998) 965–985. [MathSciNet] [Google Scholar]
  39. R.L. Pego, Front migration in the nonlinear Cahn–Hilliard equation. Proc. Roy. Soc. London, Ser. A 422 (1989) 116–133. [Google Scholar]
  40. A. Schmidt and K.G. Siebert, Design of adaptive finite element software: The finite element toolbox ALBERTA, Lect. Notes Comput. Sci. Eng. 42. Springer, Berlin (2005). [Google Scholar]
  41. B. Stoth, Convergence of the Cahn-Hilliard equation to the Mullins-Sekerka problem in spherical symmetry. J. Diff. Equ. 125 (1996) 154–183. [CrossRef] [Google Scholar]
  42. S. Tremaine, On the origin of irregular structure in Saturn's rings. Ast. J. 125 (2003) 894–901. [Google Scholar]
  43. F. Tröltzsch, Optimale Steuerung partieller Differentialgleichungen: Theorie, Verfahren und Anwendungen. Vieweg Verlag (2005). [Google Scholar]
  44. S. Zhou and M.Y. Wang, Multimaterial structural topology optimization with a generalized Cahn-Hilliard model of multiphase transition. Struct. Multidisc. Optim. 33 (2007) 89–111. [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.