메뉴 건너뛰기




Volumn 49, Issue 3, 2011, Pages 945-969

An energy stable and convergent finite-difference scheme for the modified phase field crystal equation

Author keywords

Finite difference methods; Modified Phase Field Crystal; Nonlinear partial differential equations; Phase Field Crystal; Stability

Indexed keywords

CONVEX FUNCTIONS; DAMPED WAVE EQUATIONS; DEGENERATE CASE; ERROR ESTIMATES; FINITE DIFFERENCE SCHEME; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; PHASE FIELD CRYSTAL; PHASE FIELDS; POINTWISE CONVERGENCE; SEMI-IMPLICIT; TIME LEVEL;

EID: 79960411478     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/090752675     Document Type: Article
Times cited : (331)

References (16)
  • 1
    • 35448988792 scopus 로고    scopus 로고
    • Nucleation and growth by a phase field crystal (PFC) model
    • DOI 10.1080/09500830701481737, PII 780512863
    • R. Backofen, A. Rätz, and A. Voigt, Nucleation and growth by a phase field crystal (PFC) model, Phil. Mag. Lett., 87 (2007), pp. 813-820. (Pubitemid 47621500)
    • (2007) Philosophical Magazine Letters , vol.87 , Issue.11 , pp. 813-820
    • Backofen, R.1    Ratz, A.2    Voigt, A.3
  • 2
    • 0041047822 scopus 로고
    • A second order finite difference analog of the first biharmonic boundary value problem
    • J. H. Bramble, A second order finite difference analog of the first biharmonic boundary value problem, Numer. Math., 9 (1966), pp. 236-249.
    • (1966) Numer. Math. , vol.9 , pp. 236-249
    • Bramble, J.H.1
  • 3
    • 85047687872 scopus 로고    scopus 로고
    • A linear energy stable scheme for a thin film model without slope selection
    • submitted
    • W. Chen, S. Conde, C. Wang, X. Wang, and S. Wise, A linear energy stable scheme for a thin film model without slope selection, J. Sci. Comput., submitted.
    • J. Sci. Comput.
    • Chen, W.1    Conde, S.2    Wang, C.3    Wang, X.4    Wise, S.5
  • 5
    • 1442346550 scopus 로고    scopus 로고
    • Unconditionally gradient stable time marching the Cahn-Hilliard equation
    • J. W. Bullard, R. Kalia M. Stoneham, and L. Chen, eds., Materials Research Society, Warrendale, PA
    • D. Eyre, Unconditionally gradient stable time marching the Cahn-Hilliard equation, in Computational and Mathematical Models of Microstructural Evolution 53, J. W. Bullard, R. Kalia, M. Stoneham, and L. Chen, eds., Materials Research Society, Warrendale, PA, 1998, pp. 1686-1712.
    • (1998) Computational and Mathematical Models of Microstructural Evolution , vol.53 , pp. 1686-1712
    • Eyre, D.1
  • 6
    • 0041079077 scopus 로고    scopus 로고
    • A stable and conservative finite difference scheme for the Cahn-Hilliard equation
    • D. Furihata, A stable and conservative finite difference scheme for the Cahn-Hilliard equation, Numer. Math., 87 (2001), pp. 675-699. (Pubitemid 33589610)
    • (2001) Numerische Mathematik , vol.87 , Issue.4 , pp. 675-699
    • Furihata, D.1
  • 7
    • 67349203816 scopus 로고    scopus 로고
    • Stable and efficient finite-difference nonlinear-multigrid schemes for the phase-field crystal equation
    • Z. Hu, S. M. Wise, C. Wang, and J. S. Lowengrub, Stable and efficient finite-difference nonlinear-multigrid schemes for the phase-field crystal equation, J. Comput. Phys., 228 (2009), pp. 5323-5339.
    • (2009) J. Comput. Phys. , vol.228 , pp. 5323-5339
    • Hu, Z.1    Wise, S.M.2    Wang, C.3    Lowengrub, J.S.4
  • 8
    • 0000551787 scopus 로고    scopus 로고
    • Dynamic density functional theory of liquids
    • U. Marconi and P. Tarazona, Dynamic density functional theory of liquids, J. Chem. Phys., 110 (1999), p. 8032.
    • (1999) J. Chem. Phys. , vol.110 , pp. 8032
    • Marconi, U.1    Tarazona, P.2
  • 9
    • 47049089393 scopus 로고    scopus 로고
    • Using the phase-field crystal method in the multiscale modeling of microstructure evolution
    • N. Provatas, J. Dantzig, B. Athreya, P. Chan, P. Stefanovic, N. Goldenfeld, and K. Elder, Using the phase-field crystal method in the multiscale modeling of microstructure evolution, JOM, 59 (2007), pp. 83-90.
    • (2007) JOM , vol.59 , pp. 83-90
    • Provatas, N.1    Dantzig, J.2    Athreya, J.3    Chan, P.4    Stefanovic, P.5    Goldenfeld, N.6    Elder, K.7
  • 10
    • 84861384579 scopus 로고    scopus 로고
    • Second-order convex splitting schemes for gradient flows with Ehrlich-Schwoebel type energy: Application to thin film epitaxy
    • submitted
    • J. Shen, C. Wang, X. Wang, and S. Wise, Second-order convex splitting schemes for gradient flows with Ehrlich-Schwoebel type energy: Application to thin film epitaxy, SIAM J. Numer. Anal., submitted.
    • SIAM J. Numer. Anal.
    • Shen, J.1    Wang, C.2    Wang, X.3    Wise, S.4
  • 11
    • 33745039752 scopus 로고    scopus 로고
    • Phase-field crystals with elastic interactions
    • article 225504
    • P. Stefanovic, M. Haataja, and N. Provatas, Phase-field crystals with elastic interactions, Phys. Rev. Lett., 96 (2006), article 225504.
    • (2006) Phys. Rev. Lett. , vol.96
    • Stefanovic, P.1    Haataja, M.2    Provatas, N.3
  • 12
    • 0000049185 scopus 로고
    • Hydrodynamic fluctuations at the convective instability
    • J. Swift and P. Hohenberg, Hydrodynamic fluctuations at the convective instability, Phys. Rev. A, 15 (1977), pp. 319-326.
    • (1977) Phys. Rev. A , vol.15 , pp. 319-326
    • Swift, J.1    Hohenberg, P.2
  • 13
    • 77953022743 scopus 로고    scopus 로고
    • Unconditionally stable schemes for equations of thin film epitaxy
    • C. Wang, X. Wang, and S. M. Wise, Unconditionally stable schemes for equations of thin film epitaxy, Discrete Contin. Dyn. Syst., 28 (2010), pp. 405-423.
    • Discrete Contin. Dyn. Syst. , vol.28 , Issue.2010 , pp. 405-423
    • Wang, C.1    Wang, X.2    Wise, S.M.3
  • 14
    • 79960418500 scopus 로고    scopus 로고
    • Global smooth solutions of the modified phase field crystal equation
    • C. Wang and S. Wise, Global smooth solutions of the modified phase field crystal equation, Methods Appl. Anal., 17 (2010), pp. 191-212.
    • Methods Appl. Anal. , vol.17 , Issue.2010 , pp. 191-212
    • Wang, C.1    Wise, S.2
  • 15
    • 77953019931 scopus 로고    scopus 로고
    • Unconditionally stable finite difference, nonlinear multigrid simulation of the Cahn-Hilliard-Hele-Shaw system of equations
    • S. M. Wise, Unconditionally stable finite difference, nonlinear multigrid simulation of the Cahn-Hilliard-Hele-Shaw system of equations, J. Sci. Comput., 44 (2010), pp. 38-68.
    • J. Sci. Comput. , vol.44 , Issue.2010 , pp. 38-68
    • Wise, S.M.1
  • 16
    • 77953024541 scopus 로고    scopus 로고
    • An energy-stable and convergent finite-difference scheme for the phase field crystal equation
    • S. M.Wise, C.Wang, and J. S. Lowengrub, An energy-stable and convergent finite-difference scheme for the phase field crystal equation, SIAM J. Numer. Anal., 47 (2009), pp. 2269-2288.
    • (2009) SIAM J. Numer. Anal. , vol.47 , pp. 2269-2288
    • Wise, S.M.1    Wang, C.2    Lowengrub, J.S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.