메뉴 건너뛰기




Volumn 10, Issue 1, 2008, Pages 15-43

Finite element approximation of a Cahn-Hilliard-Navier-Stokes system

Author keywords

[No Author keywords available]

Indexed keywords


EID: 42349110086     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/178     Document Type: Article
Times cited : (123)

References (31)
  • 1
    • 1542786663 scopus 로고    scopus 로고
    • Diffuse interface methods in fluid mechanics
    • MR 1609626
    • ANDERSON, D. M., MCFADDEN, G. B., & WHEELER, A. A. Diffuse interface methods in fluid mechanics. Ann. Rev. Fluid Mech. 30 (1998), 139-165. MR 1609626
    • (1998) Ann. Rev. Fluid Mech , vol.30 , pp. 139-165
    • ANDERSON, D.M.1    MCFADDEN, G.B.2    WHEELER, A.A.3
  • 2
    • 0141626836 scopus 로고    scopus 로고
    • Computation of multiphase systems with phase field models
    • Zbl 1076.76517 MR 2013023
    • BADALASSI, V. E., CENICEROS, H. D., & BANERJEE, S. Computation of multiphase systems with phase field models. J. Comput. Phys. 190 (2003), 371-397. Zbl 1076.76517 MR 2013023
    • (2003) J. Comput. Phys , vol.190 , pp. 371-397
    • BADALASSI, V.E.1    CENICEROS, H.D.2    BANERJEE, S.3
  • 3
    • 21844484383 scopus 로고
    • An error bound for the finite element approximation of the Cahn-Hilliard equation with logarithmic free energy
    • Zbl 0851.65070 MR 1359705
    • BARRETT, J. W., & BLOWEY, J. F. An error bound for the finite element approximation of the Cahn-Hilliard equation with logarithmic free energy. Numer. Math. 72 (1995), 1-20. Zbl 0851.65070 MR 1359705
    • (1995) Numer. Math , vol.72 , pp. 1-20
    • BARRETT, J.W.1    BLOWEY, J.F.2
  • 4
    • 0033450285 scopus 로고    scopus 로고
    • Finite element approximation of the Cahn-Hilliard equation with concentration mobility
    • Zbl pre01267989 MR 1609678
    • BARRETT, J. W., & BLOWEY, J. F. Finite element approximation of the Cahn-Hilliard equation with concentration mobility. Math. Comp. 68 (1999), 487-517. Zbl pre01267989 MR 1609678
    • (1999) Math. Comp , vol.68 , pp. 487-517
    • BARRETT, J.W.1    BLOWEY, J.F.2
  • 5
    • 0842303629 scopus 로고    scopus 로고
    • Finite element approximation of a sixth order nonlinear degenerate parabolic equation
    • Zbl 1041.65076 MR 2028722
    • BARRETT, J. W., LANGDON, S., & NUERNBERG, R. Finite element approximation of a sixth order nonlinear degenerate parabolic equation. Numer. Math. 96 (2004), 401-434. Zbl 1041.65076 MR 2028722
    • (2004) Numer. Math , vol.96 , pp. 401-434
    • BARRETT, J.W.1    LANGDON, S.2    NUERNBERG, R.3
  • 6
    • 0030515299 scopus 로고    scopus 로고
    • Numerical analysis of a model for phase separation of a multicomponent alloy
    • Zbl 0857.65137 MR 1367400
    • BLOWEY, J. F., COPETTI, M. I. M., & ELLIOTT, C. M. Numerical analysis of a model for phase separation of a multicomponent alloy. IMA J. Numer. Anal. 16 (1996), 111-139. Zbl 0857.65137 MR 1367400
    • (1996) IMA J. Numer. Anal , vol.16 , pp. 111-139
    • BLOWEY, J.F.1    COPETTI, M.I.M.2    ELLIOTT, C.M.3
  • 7
    • 0001766584 scopus 로고    scopus 로고
    • Mathematical study of multiphase flow under shear through order parameter formulation
    • Zbl 0937.35123 MR 1700669
    • BOYER, F. Mathematical study of multiphase flow under shear through order parameter formulation. Asymptotic Anal. 20 (1999), 175-212. Zbl 0937.35123 MR 1700669
    • (1999) Asymptotic Anal , vol.20 , pp. 175-212
    • BOYER, F.1
  • 8
    • 0036028061 scopus 로고    scopus 로고
    • BOYER, F. A theoretical and numerical model for the study of incompressible mixture flows. Comput. Fluids 31 (2002), 41-68. Zbl 1057.76060
    • BOYER, F. A theoretical and numerical model for the study of incompressible mixture flows. Comput. Fluids 31 (2002), 41-68. Zbl 1057.76060
  • 9
    • 3142696325 scopus 로고    scopus 로고
    • Numerical study of viscoelastic mixtures through a Cahn-Hilliard fluid
    • Zbl 1058.76531 MR 2077449
    • BOYER, F., CHUPIN, L., & FRANCK, B. A. Numerical study of viscoelastic mixtures through a Cahn-Hilliard fluid. Eur. J. Mech. B Fluids 23 (2004), 759-780. Zbl 1058.76531 MR 2077449
    • (2004) Eur. J. Mech. B Fluids , vol.23 , pp. 759-780
    • BOYER, F.1    CHUPIN, L.2    FRANCK, B.A.3
  • 10
    • 43449102981 scopus 로고
    • On spinodal decomposition
    • CAHN, J. W. On spinodal decomposition. Acta Metall. Mater. 9 (1961), 795-801.
    • (1961) Acta Metall. Mater , vol.9 , pp. 795-801
    • CAHN, J.W.1
  • 11
    • 33746012315 scopus 로고
    • Free energy of a nonuniform system, I, interfacial free energy
    • CAHN, J. W., & HILLIARD, J. E. Free energy of a nonuniform 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
  • 12
    • 0042762786 scopus 로고    scopus 로고
    • Existence result for a mixture of non-newtonian flows with stress diffusion using the Cahn-Hilliard formulation
    • Zbl pre01894896 MR 1951567
    • CHUPIN, L. Existence result for a mixture of non-newtonian flows with stress diffusion using the Cahn-Hilliard formulation. Discrete Contin. Dynam. Systems Ser. B 3 (2003), 45-68. Zbl pre01894896 MR 1951567
    • (2003) Discrete Contin. Dynam. Systems Ser. B , vol.3 , pp. 45-68
    • CHUPIN, L.1
  • 13
    • 0038053070 scopus 로고    scopus 로고
    • 1, 3-D; application aux equations de Maxwell.
    • Zbl 1021.78009 MR 1947708
    • 1, 3-D; application aux equations de Maxwell. C. R. Math. Acad. Sci. Paris 335 (2002), 827-832. Zbl 1021.78009 MR 1947708
    • (2002) C. R. Math. Acad. Sci. Paris , vol.335 , pp. 827-832
    • CIARLET JR., P.1    GIRAULT, V.2
  • 14
    • 29144470271 scopus 로고    scopus 로고
    • A multigrid finite element solver for the Cahn-Hilliard equation
    • Zbl 1081.65091 MR 2183612
    • KAY, D., & WELFORD, R. A multigrid finite element solver for the Cahn-Hilliard equation. J. Comput. Phys. 212 (2006), 288-304. Zbl 1081.65091 MR 2183612
    • (2006) J. Comput. Phys , vol.212 , pp. 288-304
    • KAY, D.1    WELFORD, R.2
  • 15
    • 42349102733 scopus 로고    scopus 로고
    • ELLIOTT, C. M. The Cahn-Hilliard model for the kinetics of phase separation. Mathematical Model for Phase Change Problems (Obidos, 1988), Int. Ser. Numer. Math. 88, Birkhauser, Basel (1989), 35-73. Zbl 0692.73003 MR 1038064
    • ELLIOTT, C. M. The Cahn-Hilliard model for the kinetics of phase separation. Mathematical Model for Phase Change Problems (Obidos, 1988), Int. Ser. Numer. Math. 88, Birkhauser, Basel (1989), 35-73. Zbl 0692.73003 MR 1038064
  • 16
    • 0001475208 scopus 로고    scopus 로고
    • ELLIOTT, C. M., FRENCH, D. A., & MILNER, F. A. A second order splitting method for the Cahn-Hilliard equation. Numer. Math. 54 (1989), 575-590. Zbl 0668.65097 MR 0978609
    • ELLIOTT, C. M., FRENCH, D. A., & MILNER, F. A. A second order splitting method for the Cahn-Hilliard equation. Numer. Math. 54 (1989), 575-590. Zbl 0668.65097 MR 0978609
  • 17
    • 11444270642 scopus 로고    scopus 로고
    • k Finite element analysis of a current density-electric field formulation of bean's model for superconductivity
    • Zbl 1100.78018 MR 2110240
    • ELLIOTT, C. M., KAY, D., & STYLES, V. k Finite element analysis of a current density-electric field formulation of bean's model for superconductivity. IMA J. Numer. Anal. 25 (2005), 182-204. Zbl 1100.78018 MR 2110240
    • (2005) IMA J. Numer. Anal , vol.25 , pp. 182-204
    • ELLIOTT, C.M.1    KAY, D.2    STYLES, V.3
  • 18
    • 0027811215 scopus 로고
    • The global dynamics of discrete semilinear parabolic equations
    • Zbl 0792.65066 MR 1249036
    • ELLIOTT, C. M., & STUART, A. M. The global dynamics of discrete semilinear parabolic equations. SIAM J. Numer. Anal. 30 (1993), 1622-1663. Zbl 0792.65066 MR 1249036
    • (1993) SIAM J. Numer. Anal , vol.30 , pp. 1622-1663
    • ELLIOTT, C.M.1    STUART, A.M.2
  • 19
    • 34547274225 scopus 로고    scopus 로고
    • Fully discrete finite element approximation of the Navier-Stokes-Cahn-Hilliard diffuse interface model for two-phase flows
    • Zbl pre05167765 MR 2231855
    • FENG, X. Fully discrete finite element approximation of the Navier-Stokes-Cahn-Hilliard diffuse interface model for two-phase flows. SIAM J. Numer. Anal. 44 (2006), 1049-1072. Zbl pre05167765 MR 2231855
    • (2006) SIAM J. Numer. Anal , vol.44 , pp. 1049-1072
    • FENG, X.1
  • 20
    • 15544366700 scopus 로고    scopus 로고
    • Numerical analysis of the Cahn-Hilliard equation and approximation of the Hele-Shaw problem
    • Zbl 1072.35150 MR 2126141
    • FENG, X., & PROHL, A. Numerical analysis of the Cahn-Hilliard equation and approximation of the Hele-Shaw problem. Interfaces Free Bound. 7 (2005), 1-28. Zbl 1072.35150 MR 2126141
    • (2005) Interfaces Free Bound , vol.7 , pp. 1-28
    • FENG, X.1    PROHL, A.2
  • 21
    • 42349096460 scopus 로고    scopus 로고
    • GIRAULT, V., & RAVIART, R A. Finite Element Methods for the Navier-Stokes Equations: Theory and Algorithms. Springer Ser. Comput. Math., Springer, New York, 1986. Zbl 0585.65077
    • GIRAULT, V., & RAVIART, R A. Finite Element Methods for the Navier-Stokes Equations: Theory and Algorithms. Springer Ser. Comput. Math., Springer, New York, 1986. Zbl 0585.65077
  • 22
    • 35949034972 scopus 로고
    • Theory of dynamic critical phenomena
    • HOHENBERG, P. C., & HALPERIN, B. I. Theory of dynamic critical phenomena. Rev. Mod. Phys. 49 (1977), 435-479.
    • (1977) Rev. Mod. Phys , vol.49 , pp. 435-479
    • HOHENBERG, P.C.1    HALPERIN, B.I.2
  • 23
    • 0002521331 scopus 로고    scopus 로고
    • Calculations of two-phase Navier-Stokes flows using phase-field modelling
    • Zbl 0966.76060 MR 1716497
    • JACQMIN, D. Calculations of two-phase Navier-Stokes flows using phase-field modelling. J. Comput. Phys. 155 (1999), 96-127. Zbl 0966.76060 MR 1716497
    • (1999) J. Comput. Phys , vol.155 , pp. 96-127
    • JACQMIN, D.1
  • 24
    • 0037250656 scopus 로고    scopus 로고
    • A preconditioner for the steady-state Navier-Stokes equations
    • Zbl 1013.65039 MR 1924423
    • KAY, D., LOGHIN, D., & WATHEN, A. A preconditioner for the steady-state Navier-Stokes equations. SIAM J. Sci. Comput. 24 (2002), 237-256. Zbl 1013.65039 MR 1924423
    • (2002) SIAM J. Sci. Comput , vol.24 , pp. 237-256
    • KAY, D.1    LOGHIN, D.2    WATHEN, A.3
  • 25
    • 85140866974 scopus 로고    scopus 로고
    • Efficient numerical solution of Cahn-Hilliard-Navier-Stokes fluids in 2D
    • to appear
    • KAY, D., & WELFORD, R. Efficient numerical solution of Cahn-Hilliard-Navier-Stokes fluids in 2D. SIAM J. Sci. Comput., to appear.
    • SIAM J. Sci. Comput
    • KAY, D.1    WELFORD, R.2
  • 26
    • 9644260709 scopus 로고    scopus 로고
    • A diffuse-interface model for axisymmetric immiscible two-phase flow
    • Zbl pre02132586 MR 2102831
    • KIM, J. A diffuse-interface model for axisymmetric immiscible two-phase flow. Appl. Math. Comput. 160 (2005), 589-606. Zbl pre02132586 MR 2102831
    • (2005) Appl. Math. Comput , vol.160 , pp. 589-606
    • KIM, J.1
  • 27
    • 0346332035 scopus 로고    scopus 로고
    • Conservative multigrid methods for Cahn-Hilliard fluids
    • Zbl 1109.76348 MR 2030475
    • KIM, J., KANG, K., & LOWENGRUB, J. Conservative multigrid methods for Cahn-Hilliard fluids. J. Comput. Phys. 193(2004), 511-543. Zbl 1109.76348 MR 2030475
    • (2004) J. Comput. Phys , vol.193 , pp. 511-543
    • KIM, J.1    KANG, K.2    LOWENGRUB, J.3
  • 28
    • 77956910747 scopus 로고    scopus 로고
    • LIONS, J.-L. On some questions in boundary value problems of mathematical physics. Contemporary Development in Continuum Mechanics and Partial Differential Equations (Rio de Janeiro, 1977), North-Holland Math. Stud. 30, North-Holland (1978), 284-346. Zbl 0404.35002 MR 0519648
    • LIONS, J.-L. On some questions in boundary value problems of mathematical physics. Contemporary Development in Continuum Mechanics and Partial Differential Equations (Rio de Janeiro, 1977), North-Holland Math. Stud. 30, North-Holland (1978), 284-346. Zbl 0404.35002 MR 0519648
  • 29
    • 42349109444 scopus 로고    scopus 로고
    • LIONS, J.-L., & MAGENES, E. Non-Homogeneous Boundary Value Problems and Applications. I, Springer, Berlin (1972). Zbl 0223.35039 MR 0350177
    • LIONS, J.-L., & MAGENES, E. Non-Homogeneous Boundary Value Problems and Applications. Volume I, Springer, Berlin (1972). Zbl 0223.35039 MR 0350177
  • 30
    • 42349088131 scopus 로고    scopus 로고
    • RODRIGUES, J.-F. Obstacle Problems in Mathematical Physics. North-Holland Math. Stud. 134, North-Holland, Amsterdam (1987). Zbl 0606.73017 MR 0880369
    • RODRIGUES, J.-F. Obstacle Problems in Mathematical Physics. North-Holland Math. Stud. 134, North-Holland, Amsterdam (1987). Zbl 0606.73017 MR 0880369
  • 31
    • 0000048673 scopus 로고
    • GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems
    • Zbl 0599.65018 MR 0848568
    • SAAD, Y., & SCHULTZ, M. H. GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7 (1986), 856-869. Zbl 0599.65018 MR 0848568
    • (1986) SIAM J. Sci. Statist. Comput , vol.7 , pp. 856-869
    • SAAD, Y.1    SCHULTZ, M.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.