메뉴 건너뛰기




Volumn 68, Issue 8, 2014, Pages 821-846

Second order schemes and time-step adaptivity for allen-cahn and cahn-hilliard models

Author keywords

Adaptive time stepping; Diffuse interface phase field; Energy stability; Finite elements; Unique solvability

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD;

EID: 85027948699     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2014.07.014     Document Type: Article
Times cited : (146)

References (36)
  • 2
    • 0018480694 scopus 로고
    • A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening
    • S. Allen, J.W. Cahn, A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta Metall. 27 (1979) 1084-1095
    • (1979) Acta Metall , vol.27 , pp. 1084-1095
    • Allen, S.1    Cahn, J.W.2
  • 3
    • 33746012315 scopus 로고
    • Free energy of a non-uniform system i. Interfacial free energy
    • J.W. Cahn, J.E. Hilliard, 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
    • 0027647619 scopus 로고
    • The dynamics of nucleation for the cahn-hilliard equation
    • P.W. Bates, P.C. Fife, The dynamics of nucleation for the Cahn-Hilliard equation, SIAM J. Appl. Math. 53 (1993) 990-1008
    • (1993) SIAM J. Appl. Math , vol.53 , pp. 990-1008
    • Bates, P.W.1    Fife, P.C.2
  • 5
    • 0001386608 scopus 로고
    • Nonlinear aspects of the cahn-hilliard equation
    • A. Novick-Cohen, L.A. Segel, Nonlinear aspects of the Cahn-Hilliard equation, Physica D 10 (1984) 277-298
    • (1984) Physica D , vol.10 , pp. 277-298
    • Novick-Cohen, A.1    Segel, L.A.2
  • 6
    • 21144473934 scopus 로고
    • Numerical analysis of the cahn-hilliard equation with a logarithmic free energy
    • M.I.M. Copetti, C.M. Elliott, Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy, Numer. Math. 63 (1992) 39-65
    • (1992) Numer. Math , vol.63 , pp. 39-65
    • Copetti, M.I.M.1    Elliott, C.M.2
  • 8
    • 79955469960 scopus 로고    scopus 로고
    • Provably unconditionally stable, second-order time-accurate
    • H. Gomez, T.J.R. Hughes, Provably unconditionally stable, second-order time-accurate, J. Comput. Phys. 230 (2011) 5310-5327
    • (2011) J Comput. Phys , vol.230 , pp. 5310-5327
    • Gomez, H.1    Hughes, T.J.R.2
  • 9
    • 0026238354 scopus 로고
    • Numerical analysis of a continuum model of phase transition
    • Q. Du, R.A. Nicolaides, Numerical analysis of a continuum model of phase transition, SIAM J. Numer. Anal. 28 (1991) 1310-1322
    • (1991) SIAM J. Numer. Anal , vol.28 , pp. 1310-1322
    • Du, Q.1    Nicolaides, R.A.2
  • 10
    • 0000662072 scopus 로고
    • A nonconforming finite-element method for the two-dimensional cahn-hilliard equation
    • C.M. Elliott, D.A. French, 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
    • Elliott, C.M.1    French, D.A.2
  • 11
    • 0001617217 scopus 로고
    • Numerical studies of the cahn-hilliard equation for phase separation
    • C.M. Elliott, D.A. French, 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
    • Elliott, C.M.1    French, D.A.2
  • 12
    • 0001475208 scopus 로고
    • A second order splitting method for the cahn-hilliard equation
    • C.M. Elliott, D.A. French, F.A. Milner, A second order splitting method for the Cahn-Hilliard equation, Numer. Math. 54 (1989) 575-590
    • (1989) Numer. Math , vol.54 , pp. 575-590
    • Elliott, C.M.1    French, D.A.2    Milner, F.A.3
  • 13
    • 11144340252 scopus 로고    scopus 로고
    • Error analysis of a mixed finite element method for the cahn-hilliard equation
    • X. Feng, A. Prohl, 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.1    Prohl, A.2
  • 14
    • 79960845907 scopus 로고    scopus 로고
    • Energy law preserving c0 finite element schemes for phase field models in two-phase flow computations
    • J. Hua, P. Lin, C. Liu, Q. Wang, Energy law preserving C0 finite element schemes for phase field models in two-phase flow computations, J. Comput. Phys. 230 (2011) 7115-7131
    • (2011) J. Comput. Phys , vol.230 , pp. 7115-7131
    • Hua, J.1    Lin, P.2    Liu, C.3    Wang, Q.4
  • 15
    • 36148961651 scopus 로고    scopus 로고
    • An energy law preserving c0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics
    • P. Lin, C. Liu, H. Zhang, An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics, J. Comput. Phys. 227 (2007) 1411-1427
    • (2007) J. Comput. Phys , vol.227 , pp. 1411-1427
    • Lin, P.1    Liu, C.2    Zhang, H.3
  • 16
    • 0027811215 scopus 로고
    • The global dynamics of discrete semilinear parabolic equations
    • C.M. Elliott, A.M. Stuart, The global dynamics of discrete semilinear parabolic equations, SIAM J. Numer. Anal. 30 (1993) 1622-1663
    • (1993) SIAM J. Numer. Anal , vol.30 , pp. 1622-1663
    • Elliott, C.M.1    Stuart, A.M.2
  • 18
    • 55349092697 scopus 로고    scopus 로고
    • Finite element approximations of the Ericksen-Leslie model for nematic liquid crystal flow
    • R. Becker, X. Feng, A. Prohl, Finite element approximations of the Ericksen-Leslie model for nematic liquid crystal flow, SIAM J. Numer. Anal. 46 (2008) 1704-1731
    • (2008) SIAM J. Numer. Anal , vol.46 , pp. 1704-1731
    • Becker, R.1    Feng, X.2    Prohl, A.3
  • 19
    • 34547274225 scopus 로고    scopus 로고
    • Fully discrete finite element approximations of the navier-stokes-cahn-hilliard diffuse interface model for two-phase fluid flows
    • X. Feng, Fully discrete finite element approximations of the Navier-Stokes-Cahn-Hilliard diffuse interface model for two-phase fluid flows, SIAM J. Numer. Anal. 44 (2006) 1049-1072
    • (2006) SIAM J. Numer. Anal , vol.44 , pp. 1049-1072
    • Feng, X.1
  • 20
    • 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 (1) (2010) 38-68
    • (2010) J Sci. Comput , vol.44 , Issue.1 , pp. 38-68
    • Wise, S.M.1
  • 21
    • 0346332035 scopus 로고    scopus 로고
    • Conservative multigrid methods for cahn-hilliard fluids
    • J. Kim, K. Kang, J. Lowengrub, Conservative multigrid methods for Cahn-Hilliard fluids, J. Comput. Phys. 193 (2004) 511-543
    • (2004) J. Comput. Phys , vol.193 , pp. 511-543
    • Kim, J.1    Kang, K.2    Lowengrub, J.3
  • 22
    • 77957918727 scopus 로고    scopus 로고
    • Numerical approximations of allen-cahn and cahn-hilliard equations
    • J. Shen, X. Yang, Numerical approximations of Allen-Cahn and Cahn-Hilliard equations, Discrete Contin. Dyn. Syst. 28 (2010) 1669-1691
    • (2010) Discrete Contin. Dyn. Syst , vol.28 , pp. 1669-1691
    • Shen, J.1    Yang, X.2
  • 23
    • 77954143908 scopus 로고    scopus 로고
    • Numerical studies of discrete approximations to the allen-cahn equation in the sharp interface limit
    • J. Zhang, Q. Du, Numerical studies of discrete approximations to the Allen-Cahn equation in the sharp interface limit, SIAM J. Sci. Comput. 31 (2009) 3042-3063
    • (2009) SIAM J. Sci. Comput , vol.31 , pp. 3042-3063
    • Zhang, J.1    Du, Q.2
  • 24
    • 78650568203 scopus 로고    scopus 로고
    • Finite element approximation of nematic liquid crystal flows using a saddle-point structure
    • S. Badia, F. Guillén-González, J.V. Gutiérrez-Santacreu, Finite element approximation of nematic liquid crystal flows using a saddle-point structure, J. Comput. Phys. 230 (2011) 1686-1706
    • (2011) J. Comput. Phys , vol.230 , pp. 1686-1706
    • Badia, S.1    Guillén-González, F.2    Gutiérrez-Santacreu, J.V.3
  • 25
    • 84870538130 scopus 로고    scopus 로고
    • On linear schemes for a Cahn Hilliard diffuse interface model
    • F. Guillén-González, G. Tierra, On linear schemes for a Cahn Hilliard diffuse interface model, J. Comput. Phys. 234 (2013) 140-171
    • (2013) J. Comput. Phys , vol.234 , pp. 140-171
    • Guillén-González, F.1    Tierra, G.2
  • 26
    • 44449107046 scopus 로고    scopus 로고
    • Adaptive finite element methods for cahn-hilliard equations
    • L. Banas, R. Nürnberg, Adaptive finite element methods for Cahn-Hilliard equations, J. Comput. Appl. Math. 218 (2008) 2-11
    • (2008) J. Comput. Appl. Math , vol.218 , pp. 2-11
    • Banas, L.1    Nürnberg, R.2
  • 27
    • 79956091698 scopus 로고    scopus 로고
    • Computationally efficient solution to the cahn-hilliard equation: Adaptive implicit time schemes, mesh sensitivity analysis and the 3D isoperimetric problem
    • O. Wodo, B. Ganapathysubramanian, Computationally efficient solution to the Cahn-Hilliard equation: Adaptive implicit time schemes, mesh sensitivity analysis and the 3D isoperimetric problem, J. Comput. Phys. 230 (2011) 6037-6060
    • (2011) J Comput. Phys , vol.230 , pp. 6037-6060
    • Wodo, O.1    Ganapathysubramanian, B.2
  • 29
    • 0030526461 scopus 로고    scopus 로고
    • On the Cahn-Hilliard equation with degenerate mobility
    • C.M. Elliott, H. Garcke, On the Cahn-Hilliard equation with degenerate mobility, SIAM J. Math. Anal. 27 (1996) 404-423
    • (1996) SIAM J. Math. Anal , vol.27 , pp. 404-423
    • Elliott, C.M.1    Garcke, H.2
  • 30
    • 0007425693 scopus 로고    scopus 로고
    • Finite element approximation of the cahn-hilliard equation with degenerate mobility
    • J.W. Barrett, J.F. Blowey, H. Garcke, Finite element approximation of the Cahn-Hilliard equation with degenerate mobility, SIAM J. Numer. Anal. 37 (1999) 286-318
    • (1999) SIAM J. Numer. Anal , vol.37 , pp. 286-318
    • Barrett, J.W.1    Blowey, J.F.2    Garcke, H.3
  • 31
    • 0002429428 scopus 로고
    • The Cahn-Hilliard model for the kinetics of phase separation
    • J.F. Rodrigues (Ed.), Birkhäuser-Verlag, Basel, Switzerland
    • C.M. Elliott, The Cahn-Hilliard model for the kinetics of phase separation, in: J.F. Rodrigues (Ed.), Mathematical Models for Phase Change Problems, Birkhäuser-Verlag, Basel, Switzerland, 1989
    • (1989) Mathematical Models for Phase Change Problems
    • Elliott, C.M.1
  • 33
    • 85013995016 scopus 로고    scopus 로고
    • Discontinuous galerkin finite element approximation of the cahn-hilliard equation with convection
    • D. Kay, V. Styles, E. Suli, Discontinuous Galerkin finite element approximation of the Cahn-Hilliard Equation with convection, SIAM J. Numer. Anal. 47 (2009) 2660-2685
    • (2009) SIAM J. Numer. Anal , vol.47 , pp. 2660-2685
    • Kay, D.1    Styles, V.2    Suli, E.3
  • 34
    • 84861384579 scopus 로고    scopus 로고
    • Second-order convex splitting schemes for gradient flows with enhrich-schwoebel type energy: Application to thin film epitaxy
    • J. Shen, C. Wang, X. Wang, S. Wise, Second-order convex splitting schemes for gradient flows with Enhrich-Schwoebel type energy: Application to thin film epitaxy, SIAM J. Numer. Anal. 50 (1) (2012) 105-125
    • (2012) SIAM J. Numer. Anal , vol.50 , Issue.1 , pp. 105-125
    • Shen, J.1    Wang, C.2    Wang, X.3    Wise, S.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.