Free Access
Issue
ESAIM: M2AN
Volume 43, Number 5, September-October 2009
Page(s) 1003 - 1026
DOI https://doi.org/10.1051/m2an/2009015
Published online 12 June 2009
  1. N.D. Alikakos, P.W. Bates and X.F. Chen, The convergence of solutions of the Cahn–Hilliard equation to the solution of the Hele–Shaw model. Arch. Rational Mech. Anal. 128 (1994) 165–205. [Google Scholar]
  2. Ľ. Baňas and R. Nürnberg, Adaptive finite element methods for Cahn–Hilliard equations. J. Comput. Appl. Math. 218 (2008) 2–11. [CrossRef] [MathSciNet] [Google Scholar]
  3. Ľ. Baňas and R. Nürnberg, Finite element approximation of a three dimensional phase field model for void electromigration. J. Sci. Comp. 37 (2008) 202–232. [CrossRef] [Google Scholar]
  4. Ľ. Baňas and R. Nürnberg, Phase field computations for surface diffusion and void electromigration in Formula . Comput. Vis. Sci. (2008), doi: 10.1007/s00791-008-0114-0. [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. Numer. Math. 77 (1997) 1–34. [CrossRef] [MathSciNet] [Google Scholar]
  6. 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]
  7. J.W. Barrett, R. Nürnberg and V. Styles, Finite element approximation of a phase field model for void electromigration. SIAM J. Numer. Anal. 42 (2004) 738–772. [CrossRef] [MathSciNet] [Google Scholar]
  8. 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]
  9. 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]
  10. D. Braess, A posteriori error estimators for obstacle problems – another look. Numer. Math. 101 (2005) 415–421. [CrossRef] [MathSciNet] [Google Scholar]
  11. J.W. Cahn, On spinodal decomposition. Acta Metall. 9 (1961) 795–801. [CrossRef] [Google Scholar]
  12. J.W. Cahn and J.E. Hilliard, Free energy of a non-uniform system. I. Interfacial free energy. J. Chem. Phys. 28 (1958) 258–267. [CrossRef] [Google Scholar]
  13. X. Chen, Spectrum for the Allen–Cahn, Cahn–Hilliard, and phase-field equations for generic interfaces. Comm. Partial Differ. Equ. 19 (1994) 1371–1395. [Google Scholar]
  14. Z. Chen and R.H. Nochetto, Residual type a posteriori error estimates for elliptic obstacle problems. Numer. Math. 84 (2000) 527–548. [CrossRef] [MathSciNet] [Google Scholar]
  15. P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77–84. [Google Scholar]
  16. C.M. Elliott and Z. Songmu, On the Cahn–Hilliard equation. Arch. Rational Mech. Anal. 96 (1986) 339–357. [CrossRef] [MathSciNet] [Google Scholar]
  17. C.M. Elliott, D.A. French and F.A. Milner, A second order splitting method for the Cahn–Hilliard equation. Numer. Math. 54 (1989) 575–590. [CrossRef] [MathSciNet] [Google Scholar]
  18. X. Feng and A. Prohl, Error analysis of a mixed finite element method for the Cahn–Hilliard equation. Numer. Math. 99 (2004) 47–84. [CrossRef] [MathSciNet] [Google Scholar]
  19. X. Feng and H. Wu, A posteriori error estimates for finite element approximations of the Cahn–Hilliard equation and the Hele–Shaw flow. J. Comput. Math. 26 (2008) 767–796. [MathSciNet] [Google Scholar]
  20. M. Hintermüller and R.H.W. Hoppe, Goal-oriented adaptivity in control constrained optimal control of partial differential equations. SIAM J. Control Optim. 47 (2008) 1721–1743. [CrossRef] [MathSciNet] [Google Scholar]
  21. M. Hintermüller, R.H.W. Hoppe, Y. Iliash and M. Kieweg, An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints. ESAIM: COCV 14 (2008) 540–560. [CrossRef] [EDP Sciences] [Google Scholar]
  22. 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]
  23. L. Modica, Gradient theory of phase transitions with boundary contact energy. Ann. Inst. H. Poincaré Anal. Non Linéaire 4 (1987) 487–512. [Google Scholar]
  24. K.-S. Moon, R.H. Nochetto, T. von Petersdorff and C.-S. Zhang, A posteriori error analysis for parabolic variational inequalities. ESAIM: M2AN 41 (2007) 485–511. [CrossRef] [EDP Sciences] [Google Scholar]
  25. R.H. Nochetto and L.B. Wahlbin, Positivity preserving finite element approximation. Math. Comp. 71 (2002) 1405–1419. [CrossRef] [MathSciNet] [Google Scholar]
  26. R.L. Pego, Front migration in the nonlinear Cahn-Hilliard equation. Proc. Roy. Soc. London Ser. A 422 (1989) 261–278. [CrossRef] [MathSciNet] [Google Scholar]
  27. A. Veeser, Efficient and reliable a posteriori error estimators for elliptic obstacle problems. SIAM J. Numer. Anal. 39 (2001) 146–167. [CrossRef] [MathSciNet] [Google Scholar]
  28. A. Veeser, On a posteriori error estimation for constant obstacle problems, in Numerical methods for viscosity solutions and applications (Heraklion, 1999), M. Falcone and C. Makridakis Eds., Ser. Adv. Math. Appl. Sci. 59, World Sci. Publ., River Edge, USA (2001) 221–234. [Google Scholar]
  29. R. Verfürth, A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Teubner-Wiley, New York (1996). [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