A class of stable spectral methods for the Cahn-Hilliard equation

Journal of Computational Physics

Volumn 228, Issue 14, 2009, Pages 5101-5110

  He, Li ping ^a   Liu, Yunxian ^b  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b SHANDONG UNIVERSITY   (China)

Author keywords

Cahn Hilliard model; Dissipative spectral method

Indexed keywords

CAHN-HILLIARD EQUATION; CAHN-HILLIARD MODEL; DISSIPATIVE SPECTRAL METHOD; FOURIER; FULLY DISCRETE; INITIAL-BOUNDARY VALUE PROBLEMS; PREDICTION-CORRECTION; SEMI-IMPLICIT; SPECTRAL METHODS; TWO-DIMENSIONAL;

INITIAL VALUE PROBLEMS;

EID: 67349192151     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.04.011     Document Type: Article

References (27)

1. Barrett J.W., Blowey J.F., and Garcke H. On fully practical finite element approximations of degenerate Cahn-Hilliard systems. M2AN Math. Model. Numer. Anal. 35 (2001) 713-748
2. Boyd J.P. Chebyshev and Fourier Spectral Methods. second ed. (2001), Dover, Mineola, NY
3. Cahn J.W., and Hilliard J.E. Free energy of a non-uniform system I: interfacial free energy. J. Chem. Phys. 28 (1958) 258-267
4. Chen L.Q., and Shen J. Application of semi-implicit Fourier-spectral method to phase field equations. Comput. Phys. Comm. 108 (1998) 147-158
5. Cheng M., and Warren J.A. An efficient algorithm for solving the phase field crystal model. J. Comput. Phys. 227 (2008) 6241-6248
6. Coasta B., Don W.-S., Gottlieb D., and Sendersky R. Two-dimensional multi-domain hybrid spectral-WENO methods for conservation laws. Commun. Comput. Phys. 1 (2006) 550-577
7. Copetti M.I.M., and Elliot C.M. Kinetics of phase decomposition processes: numerical solutions to Cahn-Hilliard equation. Mater. Sci. Technol. 6 (1990) 273-283
8. Elliot C.M., and French D.A. Numerical studies of the Cahn-Hilliard equation for phase separation. IMA J. Appl. Math. 38 (1987) 97-128
9. Elliot C.M., and French D.A. A nonconforming finite element method for the two dimensional Cahn-Hilliard equation. SIAM J. Numer. Anal. 26 (1989) 884-903
10. Elliot C.M., French D.A., and Milner D.A. A second order splitting method for the Cahn-Hilliard equation. Numer. Math. 54 (1989) 575-590
11. Elliot C.M., and Larsson S. Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation for phase separation. Math. Comp. 58 (1992) 603-630
12. Eyre D.J. In: Bullard J.W., et al. (Ed). Computational and Mathematical Models of Microstructural Evolution (1998), Materials Research Society, Warrendale, PA 39-46
13. D.J. Eyre. .
14. Feng X.B., and Prohl A. Error analysis of a mixed finite element method for the Cahn-Hilliard equation. Numer. Math. 99 (2004) 47-84
15. Furihata D. A stable and conservative finite difference scheme for the Cahn-Hilliard equation. Numer. Math. 87 (2001) 675-699
16. Gurtin M.E. On the two-phase Stephan problem with interfacial energy and entropy. Acta Rat. Mech. Anal. 96 (1988) 199-243
17. He L.-P., Mao D.-K., and Guo B.-Y. Prediction-correction Legendre spectral scheme for incompressible fluid flow. M2AN Math. Model. Numer. Anal. 33 (1999) 113-120
18. He Y.N., Liu Y.X., and Tang T. On large time-stepping methods for the Cahn-Hilliard equation. Appl. Numer. Math. 57 (2007) 616-628
19. He Y.N., and Liu Y.X. Stability and convergence of the spectral Galerkin method for the Cahn-Hilliard equation. Numer. Meth. PDEs 24 (2008) 1485-1500
20. Mello E.V.L., and Filho O.T.S. Numerical study of the Cahn-Hilliard equation in one, two and three dimensions. Phys. A 347 (2005) 429-443
21. Pego R.L. Front migration in the nonlinear Cahn-Hilliard equation. Proc. Roy. Soc. London A 422 (1989) 261-278
22. Sun Z.Z. A second-order accurate linearized difference scheme for the two-dimensional Cahn-Hilliard equation. Math. Comp. 64 (1995) 1463-1471
23. Vollmayr-Lee B.P., and Rutenberg A.D. Fast and accurate coarsening simulation with an unconditionally stable time step. Phys. Rev. E 68 0066703 (2003) 13
24. Wang Y., Chen L.-Q., and Khachaturyan A.G. Kinetics of strain-induced morphological transformation in cubic alloys with a miscibility gap. Acta Metall. Mater. 41 (1993) 279-296
25. Xiu D., and Shen J. An efficient spectral method for acoustic scattering from rough surfaces. Commun. Comput. Phys. 1 (2007) 54-72
26. Xu C., and Tang T. Stability analysis of large time-stepping methods for epitaxial growth models. SIAM J. Numer. Anal. 44 (2006) 1759-1779
27. Zhu J., Chen L.-Q., Shen J., and Tikare V. Coarsening kinetics from a variable-mobility Cahn-Hilliard equation: application of a semi-implicit Fourier spectral method. Phys. Rev. E 60 (1999) 3564-3572