메뉴 건너뛰기




Volumn 57, Issue 5-7 SPEC. ISS., 2007, Pages 616-628

On large time-stepping methods for the Cahn-Hilliard equation

Author keywords

Cahn Hilliard equation; Decay of energy; Large time stepping method; Semi implicit scheme; Spectral method; Stability

Indexed keywords

FINITE DIFFERENCE METHOD; SYSTEM STABILITY;

EID: 34147135231     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2006.07.026     Document Type: Article
Times cited : (220)

References (23)
  • 1
    • 0035537706 scopus 로고    scopus 로고
    • On fully practical finite element approximations of degenerate Cahn-Hilliard systems
    • 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
    • (2001) M2AN Math. Model. Numer. Anal. , vol.35 , pp. 713-748
    • Barrett, J.W.1    Blowey, J.F.2    Garcke, H.3
  • 3
    • 33746012315 scopus 로고
    • Free energy of a non-uniform system I: Interfacial free energy
    • 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
    • (1958) J. Chem. Phys. , vol.28 , pp. 258-267
    • Cahn, J.W.1    Hilliard, J.E.2
  • 4
    • 33846342598 scopus 로고    scopus 로고
    • Two-dimensional multi-domain hybrid spectral-WENO methods for conservation laws
    • Costa 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
    • (2006) Commun. Comput. Phys. , vol.1 , pp. 550-577
    • Costa, B.1    Don, W.-S.2    Gottlieb, D.3    Sendersky, R.4
  • 5
    • 0001617217 scopus 로고
    • Numerical studies of the Cahn-Hilliard equation for phase separation
    • 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
    • (1987) IMA J. Appl. Math. , vol.38 , pp. 97-128
    • Elliot, C.M.1    French, D.A.2
  • 6
    • 0000662072 scopus 로고
    • A nonconforming finite element method for the two-dimensional Cahn-Hilliard equation
    • 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
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 884-903
    • Elliot, C.M.1    French, D.A.2
  • 7
    • 0001475208 scopus 로고
    • A second order splitting method for the Cahn-Hilliard equation
    • 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
    • (1989) Numer. Math. , vol.54 , pp. 575-590
    • Elliot, C.M.1    French, D.A.2    Milner, D.A.3
  • 8
    • 84968516048 scopus 로고
    • Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation
    • Elliot C.M., and Larsson S. Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation. Math. Comp. 58 (1992) 603-630
    • (1992) Math. Comp. , vol.58 , pp. 603-630
    • Elliot, C.M.1    Larsson, S.2
  • 9
    • 0001152970 scopus 로고    scopus 로고
    • Applications of semi-implicit Fourier-spectral method to phase field equations
    • Chen L.Q., and Shen J. Applications of semi-implicit Fourier-spectral method to phase field equations. Comput. Phys. Comm. 108 (1998) 147-158
    • (1998) Comput. Phys. Comm. , vol.108 , pp. 147-158
    • Chen, L.Q.1    Shen, J.2
  • 10
    • 11144340252 scopus 로고    scopus 로고
    • Error analysis of a mixed finite element method for the Cahn-Hilliard equation
    • 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
    • (2004) Numer. Math. , vol.99 , pp. 47-84
    • Feng, X.B.1    Prohl, A.2
  • 11
    • 0041079077 scopus 로고    scopus 로고
    • A stable and conservative finite difference scheme for the Cahn-Hilliard equation
    • Furihata D. A stable and conservative finite difference scheme for the Cahn-Hilliard equation. Numer. Math. 87 (2001) 675-699
    • (2001) Numer. Math. , vol.87 , pp. 675-699
    • Furihata, D.1
  • 12
    • 0022876407 scopus 로고
    • On the two-phase Stephan problem with interfacial energy and entropy
    • Gurtin M.E. On the two-phase Stephan problem with interfacial energy and entropy. Acta Rat. Mech. Anal. 96 (1988) 199-243
    • (1988) Acta Rat. Mech. Anal. , vol.96 , pp. 199-243
    • Gurtin, M.E.1
  • 13
    • 17744382165 scopus 로고    scopus 로고
    • Asymptotic behavior and time discretization analysis for the nonstationary Navier-Stokes problem
    • He Y.N., and Li K.T. Asymptotic behavior and time discretization analysis for the nonstationary Navier-Stokes problem. Numer. Math. 98 4 (2004) 647-673
    • (2004) Numer. Math. , vol.98 , Issue.4 , pp. 647-673
    • He, Y.N.1    Li, K.T.2
  • 14
    • 0032364016 scopus 로고    scopus 로고
    • Convergence and stability of finite element nonlinear Galerkin method for the Navier-Stokes equations
    • He Y.N., and Li K.T. Convergence and stability of finite element nonlinear Galerkin method for the Navier-Stokes equations. Numer. Math. 79 (1998) 77-106
    • (1998) Numer. Math. , vol.79 , pp. 77-106
    • He, Y.N.1    Li, K.T.2
  • 15
    • 34147123335 scopus 로고    scopus 로고
    • Y.N. He, Y.X. Liu, Stability and convergence of the spectral Galerkin method for the Cahn-Hilliard equation, in preparation
  • 16
    • 1142290702 scopus 로고    scopus 로고
    • Thin film epitaxy with or without slope selection
    • Li B., and Liu J.G. Thin film epitaxy with or without slope selection. Eur. J. Appl. Math. 14 (2003) 713-743
    • (2003) Eur. J. Appl. Math. , vol.14 , pp. 713-743
    • Li, B.1    Liu, J.G.2
  • 17
    • 10844251567 scopus 로고    scopus 로고
    • Numerical study of the Cahn-Hilliard equation in one, two and three dimensions
    • 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
    • (2005) Phys. A , vol.347 , pp. 429-443
    • Mello, E.V.L.1    Filho, O.T.S.2
  • 18
    • 0001410452 scopus 로고
    • Front migration in the nonlinear Cahn-Hilliard equation
    • Pego R.L. Front migration in the nonlinear Cahn-Hilliard equation. Proc. Roy. Soc. London A 422 (1989) 261-278
    • (1989) Proc. Roy. Soc. London A , vol.422 , pp. 261-278
    • Pego, R.L.1
  • 19
    • 21844485652 scopus 로고
    • A second-order accurate linearized difference scheme for the two-dimensional Cahn-Hilliard equation
    • Sun Z.Z. A second-order accurate linearized difference scheme for the two-dimensional Cahn-Hilliard equation. Math. Comp. 64 (1995) 1463-1471
    • (1995) Math. Comp. , vol.64 , pp. 1463-1471
    • Sun, Z.Z.1
  • 21
    • 34147178547 scopus 로고    scopus 로고
    • An efficient spectral method for acoustic scattering from rough surfaces
    • Xiu D., and Shen J. An efficient spectral method for acoustic scattering from rough surfaces. Commun. Comput. Phys. 1 (2007) 54-72
    • (2007) Commun. Comput. Phys. , vol.1 , pp. 54-72
    • Xiu, D.1    Shen, J.2
  • 22
    • 34547512592 scopus 로고    scopus 로고
    • C. Xu, T. Tang, Stability analysis of large time-stepping methods for epitaxial growth models, SIAM J. Numer. Anal. (2006), in prress
  • 23
    • 0000707473 scopus 로고    scopus 로고
    • Coarsening kinetics from a variable-mobility Cahn-Hilliard equation: Application of a semi-implicit Fourier spectral method
    • 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 4 (1999) 3564-3572
    • (1999) Phys. Rev. E , vol.60 , Issue.4 , pp. 3564-3572
    • Zhu, J.1    Chen, L.-Q.2    Shen, J.3    Tikare, V.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.