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Volumn 230, Issue 4, 2011, Pages 1686-1706

Finite element approximation of nematic liquid crystal flows using a saddle-point structure

Author keywords

Ericksen Leslie problem; Finite element methods; Ginzburg Landau problem; Nematic liquid crystals; Saddle point problems

Indexed keywords

CRYSTAL STRUCTURE; LAGRANGE MULTIPLIERS; NEMATIC LIQUID CRYSTALS; NEWTON-RAPHSON METHOD;

EID: 78650568203     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.11.033     Document Type: Article
Times cited : (102)

References (31)
  • 1
    • 0000631032 scopus 로고    scopus 로고
    • A new algorithm for computing liquid crystal stable configurations: the harmonic mapping case
    • Alouges F. A new algorithm for computing liquid crystal stable configurations: the harmonic mapping case. SIAM J. Numer. Anal. 1997, 34(5):1708-1726.
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.5 , pp. 1708-1726
    • Alouges, F.1
  • 2
    • 38349076060 scopus 로고    scopus 로고
    • A convergent and constraint-preserving finite element method for the p-harmonic flow into spheres
    • Barrett J.W., Bartels S., Feng X., Prohl A. A convergent and constraint-preserving finite element method for the p-harmonic flow into spheres. SIAM J. Numer. Anal. 2007, 45(3):905-927.
    • (2007) SIAM J. Numer. Anal. , vol.45 , Issue.3 , pp. 905-927
    • Barrett, J.W.1    Bartels, S.2    Feng, X.3    Prohl, A.4
  • 3
    • 33644536096 scopus 로고    scopus 로고
    • Stability and convergence of finite-element approximation schemes for harmonic maps
    • Bartels S. Stability and convergence of finite-element approximation schemes for harmonic maps. SIAM J. Numer. Anal. 2005, 43(1):220-238.
    • (2005) SIAM J. Numer. Anal. , vol.43 , Issue.1 , pp. 220-238
    • Bartels, S.1
  • 4
    • 55349092697 scopus 로고    scopus 로고
    • Finite element approximations of the Ericksen-Leslie model for nematic liquid crystal flow
    • Becker R., Feng X., Prohl A. Finite element approximations of the Ericksen-Leslie model for nematic liquid crystal flow. SIAM J. Numer. Anal. 2008, 46(4):1704-1731.
    • (2008) SIAM J. Numer. Anal. , vol.46 , Issue.4 , pp. 1704-1731
    • Becker, R.1    Feng, X.2    Prohl, A.3
  • 8
    • 77952736810 scopus 로고    scopus 로고
    • Galerkin finite element methods with symmetric pressure stabilization for the transient Stokes equations: stability and convergence analysis
    • Burman E., Fernández M.A. Galerkin finite element methods with symmetric pressure stabilization for the transient Stokes equations: stability and convergence analysis. SIAM J. Numer. Anal. 2008, 47(1):409-439.
    • (2008) SIAM J. Numer. Anal. , vol.47 , Issue.1 , pp. 409-439
    • Burman, E.1    Fernández, M.A.2
  • 9
    • 4243434882 scopus 로고    scopus 로고
    • Monte Carlo simulations of stable point defects in hybrid nematic films
    • Chiccoli C., Lavrentovich O.D., Pasini P., Zannoni C. Monte Carlo simulations of stable point defects in hybrid nematic films. Phys. Rev. Lett. 1997, 79(22):4401-4404.
    • (1997) Phys. Rev. Lett. , vol.79 , Issue.22 , pp. 4401-4404
    • Chiccoli, C.1    Lavrentovich, O.D.2    Pasini, P.3    Zannoni, C.4
  • 11
    • 0023172883 scopus 로고
    • Continuum theory of nematic liquid crystals
    • Ericksen J. Continuum theory of nematic liquid crystals. Res. Mech. 1987, 21:381-392.
    • (1987) Res. Mech. , vol.21 , pp. 381-392
    • Ericksen, J.1
  • 12
    • 0002742450 scopus 로고
    • Conservation laws for liquid crystals
    • Ericksen J.L. Conservation laws for liquid crystals. Trans. Soc. Rheol. 1961, 5:22-34.
    • (1961) Trans. Soc. Rheol. , vol.5 , pp. 22-34
    • Ericksen, J.L.1
  • 14
    • 0344063595 scopus 로고    scopus 로고
    • Orientational defects near colloidal particles in a nematic liquid crystal
    • Feng J.J., Zhou C. Orientational defects near colloidal particles in a nematic liquid crystal. J. Colloid Interface Sci. 2004, 269:72-78.
    • (2004) J. Colloid Interface Sci. , vol.269 , pp. 72-78
    • Feng, J.J.1    Zhou, C.2
  • 15
    • 0008820036 scopus 로고
    • On the theory of liquid crystals
    • Frank F.C. On the theory of liquid crystals. Discuss. Faraday Soc. 1958, 25:19-28.
    • (1958) Discuss. Faraday Soc. , vol.25 , pp. 19-28
    • Frank, F.C.1
  • 16
    • 85189836815 scopus 로고    scopus 로고
    • Mixed formulation, approximation and decoupling algorithm for a penalized nematic liquid crystals model. Mathematics of Computation, (in press).
    • V. Girault, F. Guillén-González. Mixed formulation, approximation and decoupling algorithm for a penalized nematic liquid crystals model. Mathematics of Computation, (in press).
    • Girault, V.1    Guillén-González, F.2
  • 17
    • 85189840870 scopus 로고    scopus 로고
    • A linear mixed finite element scheme for a nematic Ericksen-Leslie liquid crystal model. submitted for publication.
    • F. Guillén-González, J.V. Gutiérrez-Santacreu. A linear mixed finite element scheme for a nematic Ericksen-Leslie liquid crystal model. submitted for publication.
    • Guillén-González, F.1    Gutiérrez-Santacreu, J.V.2
  • 18
    • 0000966077 scopus 로고
    • Finite element approximation of the nonstationary Navier-Stokes problem. I: Regularity of solutions and second-order error estimates for spatial discretization
    • Heywood J.G., Rannacher R. Finite element approximation of the nonstationary Navier-Stokes problem. I: Regularity of solutions and second-order error estimates for spatial discretization. SIAM J. Numer. Anal. 1982, 19:275-311.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 275-311
    • Heywood, J.G.1    Rannacher, R.2
  • 19
    • 78650528002 scopus 로고    scopus 로고
    • A saddle-point approach to the computation of harmonic maps
    • Hu Q., Tai X.-C., Winther R. A saddle-point approach to the computation of harmonic maps. SIAM J. Numer. Anal. 2009, 47(2):1500-1523.
    • (2009) SIAM J. Numer. Anal. , vol.47 , Issue.2 , pp. 1500-1523
    • Hu, Q.1    Tai, X.-C.2    Winther, R.3
  • 20
    • 0039210049 scopus 로고
    • Some constitutive equations for liquid crystals
    • Leslie F. Some constitutive equations for liquid crystals. Arch. Ration. Mech. Anal. 1968, 28:265-283.
    • (1968) Arch. Ration. Mech. Anal. , vol.28 , pp. 265-283
    • Leslie, F.1
  • 21
    • 0002397231 scopus 로고
    • Theory of flow phenomena in liquid crystals
    • Leslie F.M. Theory of flow phenomena in liquid crystals. Adv. Liq. Cryst. 1979, 4:1-81.
    • (1979) Adv. Liq. Cryst. , vol.4 , pp. 1-81
    • Leslie, F.M.1
  • 22
    • 84990553603 scopus 로고
    • Nonlinear theory of defects in nematic liquid crystals: phase transition and flow phenomena
    • Lin F.H. Nonlinear theory of defects in nematic liquid crystals: phase transition and flow phenomena. Commun. Pure Appl. Math. 1989, 42:789-814.
    • (1989) Commun. Pure Appl. Math. , vol.42 , pp. 789-814
    • Lin, F.H.1
  • 23
    • 33645888383 scopus 로고    scopus 로고
    • Simulations of singularity dynamics in liquid crystal flows: a C0 finite element approach
    • Lin P., Liu C. Simulations of singularity dynamics in liquid crystal flows: a C0 finite element approach. J. Comput. Phys. 2006, 215:348-362.
    • (2006) J. Comput. Phys. , vol.215 , pp. 348-362
    • Lin, P.1    Liu, C.2
  • 24
    • 36148961651 scopus 로고    scopus 로고
    • An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics
    • Lin P., Liu C., Zhang H. An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics. J. Comput. Phys. 2007, 227(2):1411-1427.
    • (2007) J. Comput. Phys. , vol.227 , Issue.2 , pp. 1411-1427
    • Lin, P.1    Liu, C.2    Zhang, H.3
  • 25
    • 0000002009 scopus 로고    scopus 로고
    • Approximation of liquid crystal flows
    • Liu C., Walkington N.J. Approximation of liquid crystal flows. SIAM J. Numer. Anal. 2000, 37(3):725-741.
    • (2000) SIAM J. Numer. Anal. , vol.37 , Issue.3 , pp. 725-741
    • Liu, C.1    Walkington, N.J.2
  • 26
    • 0035999311 scopus 로고    scopus 로고
    • Mixed methods for the approximation of liquid crystal flows
    • Liu C., Walkington N.J. Mixed methods for the approximation of liquid crystal flows. Math. Model. Numer. Anal. 2002, 36(2):205-222.
    • (2002) Math. Model. Numer. Anal. , vol.36 , Issue.2 , pp. 205-222
    • Liu, C.1    Walkington, N.J.2
  • 27
    • 37049160761 scopus 로고
    • Theory of liquid crystals
    • Oseen C. Theory of liquid crystals. Trans. Faraday Soc. 1933, 29:883-899.
    • (1933) Trans. Faraday Soc. , vol.29 , pp. 883-899
    • Oseen, C.1
  • 28
    • 0002554358 scopus 로고
    • Motion of interacting point defects in nematics
    • Pismen L.M., Rubinstein B.Y. Motion of interacting point defects in nematics. Phys. Rev. Lett. 1992, 69(1).
    • (1992) Phys. Rev. Lett. , vol.69 , Issue.1
    • Pismen, L.M.1    Rubinstein, B.Y.2
  • 30
    • 33744825719 scopus 로고    scopus 로고
    • Annihilation of nematic point defects: Pre-collision and post-collision evolution
    • Svetec M., Kralj S., Bradač Z., Žumer S. Annihilation of nematic point defects: Pre-collision and post-collision evolution. The Eur. Phys. J. 2006, 20(E):71-79.
    • (2006) The Eur. Phys. J. , vol.20 , Issue.E , pp. 71-79
    • Svetec, M.1    Kralj, S.2    Bradač, Z.3    Žumer, S.4


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