Free Access
Issue |
ESAIM: M2AN
Volume 45, Number 3, May-June 2011
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Page(s) | 523 - 540 | |
DOI | https://doi.org/10.1051/m2an/2010065 | |
Published online | 30 November 2010 |
- L. Baňas, A. Prohl and R. Schätzle, Finite element approximations of harmonic map heat flows and wave map into spheres of nonconstant radii. Numer. Math. 115 (2010) 395–432. [CrossRef] [MathSciNet] [Google Scholar]
- J.W. Barrett, X. Feng and A. Prohl, Convergence of a fully discrete finite element method for a degenerate parabolic system modelling nematic liquid crystals with variable degree of orientation. Math. Model. Numer. Anal. 40 (2006) 175–199. [Google Scholar]
- R. Becker, X. Feng and A. Prohl, Finite element approximations of the Ericksen-Leslie model for nematic liquid crystal flow. SIAM J. Numer. Anal. 46 (2008) 1704–1731. [CrossRef] [MathSciNet] [Google Scholar]
- F. Bethuel, H. Brezis and F. Helein, Ginzburg-Landau Vorticies. Kluwer (1995). [Google Scholar]
- R. Cohen, R. Hardt, D. Kinderlehrer, S. Lin and M. Luskin, Minimum energy configurations for liquid crystals: Computational results, in Theory and Applications of Liquid Crystals, J.L. Ericksen and D. Kinderlehrer Eds., The IMA Volumes in Mathematics and its Applications 5, Springer-Verlag, New York (1987). [Google Scholar]
- Q. Du, B. Guo and J. Shen, Fourier spectral approximation to a dissipative system modeling the flow of liquid crystals. SIAM J. Numer. Anal. 39 (2001) 735–762. [CrossRef] [MathSciNet] [Google Scholar]
- F. Duzaar, J. Kristensen and G. Mingione, The existence of regular boundary points for non-linear elliptic systems. J. Reine Angew. Math. 602 (2007) 17–58. [CrossRef] [MathSciNet] [Google Scholar]
- J. Ericksen, Conservation laws for liquid crystals. Trans. Soc. Rheol. 5 (1961) 22–34. [Google Scholar]
- J. Ericksen, Nilpotent energies in liquid crystal theory. Arch. Rational Mech. Anal. 10 (1962) 189–196. [CrossRef] [MathSciNet] [Google Scholar]
- J. Ericksen, Continuum theory of nematic liquid crystals. Res. Mechanica 21 (1987) 381–392. [Google Scholar]
- F.C. Frank, On the theory of liquid crystals. Discuss. Faraday Soc. 25 (1958) 19–28. [Google Scholar]
- G.P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations I: Linearized steady problems, Springer Tracts in Natural Philosophy 38. Springer-Verlag, New York (1994). [Google Scholar]
- V. Girault and F. Guillén-González, Mixed formulation, approximation and decoupling algorithm for a penalized nematic liquid crystals model. Preprint (2009). [Google Scholar]
- V. Girault, R.H. Nochetto and R. Scott, Maximum-norm stability of the finite element Stokes projection. J. Math. Pures Appl. 84 (2005) 279–330. [CrossRef] [MathSciNet] [Google Scholar]
- R. Hardt and D. Kinderlehrer, Mathematical questions of liquid crystal theory, in Theory and Applications of Liquid Crystals, J.L. Ericksen and D. Kinderlehrer Eds., The IMA Volumes in Mathematics and its Applications 5, Springer-Verlag, New York (1987). [Google Scholar]
- R. Hardt and F.H. Lin, Stability of singularities of minimizing harmonic maps. J. Differential Geom. 29 (1989) 113–123. [MathSciNet] [Google Scholar]
- R. Hardt, D. Kinderlehrer and F.H. Lin, Existence and partial regularity of static liquid crystal configurations. Comm. Math. Phys. 105 (1986) 547–570. [Google Scholar]
- Q. Hu, X.-C. Tai and R. Winther, A saddle point approach to the computation of harmonic maps. SIAM J. Numer. Anal. 47 (2009) 1500–1523. [CrossRef] [MathSciNet] [Google Scholar]
- R. Jerard and M. Soner, Dynamics of Ginzburg-Landau vortices. Arch. Rational Mech. Anal. 142 (1998) 99–125. [CrossRef] [MathSciNet] [Google Scholar]
- F. Leslie, Some constitutive equations for liquid crystals. Arch. Rational Mech. Anal. 28 (1968) 265–283. [Google Scholar]
- F. Leslie, Theory of flow phenomenum in liquid crystals, in The Theory of Liquid Crystals 4, W. Brown Ed., Academic Press, New York (1979) 1–81. [Google Scholar]
- F.H. Lin, Mathematics theory of liquid crystals, in Applied Mathematics At The Turn Of Century: Lecture notes of the 1993 summer school, Universidat Complutense de Madrid (1995). [Google Scholar]
- F.H. Lin, Solutions of Ginzburg-Landau equations and critical points of renormalized energy. Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995) 599–622. [Google Scholar]
- F.H. Lin, Some dynamic properties of Ginzburg-Landau vorticies. Comm. Pure Appl. Math. 49 (1996) 323–359. [CrossRef] [MathSciNet] [Google Scholar]
- F.H. Lin and C. Liu, Nonparabolic dissipative systems, modeling the flow of liquid crystals. Comm. Pure Appl. Math. XLVIII (1995) 501–537. [Google Scholar]
- F.H. Lin and C. Liu, Existence of solutions for the Ericksen-Leslie system. Arch. Rational Mech. Anal. 154 (2000) 135–156. [Google Scholar]
- P. Lin, C. Liu and 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. [CrossRef] [MathSciNet] [Google Scholar]
- C. Liu and N.J. Walkington, Approximation of liquid crystal flows. SIAM J. Numer. Anal. 37 (2000) 725–741. [CrossRef] [MathSciNet] [Google Scholar]
- C. Liu and N.J. Walkington, Mixed Methods for the Approximation of Liquid Crystal Flows. ESAIM: M2AN 36 (2002) 205–222. [CrossRef] [EDP Sciences] [Google Scholar]
- G. Mingione, Regularity of minima: an invitation to the dark side of the calculus of variations. Appl. Math. 51 (2006) 355–426. [CrossRef] [MathSciNet] [Google Scholar]
- C.W. Oseen, The theory of liquid crystals. Trans. Faraday Soc. 29 (1933) 883–889. [Google Scholar]
- I.W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals: a Mathematical Introduction. Taylor & Francis Inc., New York (2004). [Google Scholar]
- E.G. Virga, Variational theories for liquid crystals, Appl. Math. Math. Comput. 8. Chapman & Hall, London (1994). [Google Scholar]
- N.J. Walkington, Compactness properties of the DG and CG time stepping schemes for parabolic equations. SIAM J. Numer. Anal. 47 (2010) 4680–4710. [CrossRef] [MathSciNet] [Google Scholar]
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