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All issues Volume 47 / No 5 (September-October 2013) ESAIM: M2AN, 47 5 (2013) 1433-1464 References
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Issue
ESAIM: M2AN
Volume 47, Number 5, September-October 2013
Page(s) 1433 - 1464
DOI https://doi.org/10.1051/m2an/2013076
Published online 30 July 2013
  1. F. Alouges, A new algorithm for computing liquid crystal stable configurations: the harmonic mapping case. SIAM J. Numer. Anal. 34 (1997) 1708–1726. [CrossRef] [MathSciNet] [Google Scholar]
  2. P. Azérad and F. Guillen-González, Mathematical justification of the hydrostatic approximation in the primitive equations of geophysical fluid dynamics. SIAM J. Math. Anal. 33 (2001) 847–859. [CrossRef] [MathSciNet] [Google Scholar]
  3. 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]
  4. B. Climent-Ezquerra, F. Guillén-González and M. Rojas-Medar, Reproductivity for a nematic liquid crystal model. Z. Angew. Math. Phys. (2006) 984–998. [Google Scholar]
  5. Y.M. Chen, The weak solutions to the evolution problems of harmonic maps. Math. Z. 201 (1989) 69–74. [CrossRef] [MathSciNet] [Google Scholar]
  6. P.G. Ciarlet, The finite element method for elliptic problems. Amsterdam, North-Holland (1987). [Google Scholar]
  7. J.J. Douglas, T. Dupont and L. Wahlbin, The stability in Lq of the L2-projection into finite element function spaces. Numer. Math. 23 (1974/75) 193–197. [Google Scholar]
  8. V. Girault and F. Guillén-González, Mixed formulation, approximation and decoupling algorithm for a nematic liquid crystals model. Math. Comput. 80 (2011) 781–819. [CrossRef] [Google Scholar]
  9. V. Girault, N. Nochetto and R. Scott, Estimates of the finite element Stokes projection in W1,∞. C. R. Math. Acad. Sci. Paris 338 (2004) 957–962. [CrossRef] [MathSciNet] [Google Scholar]
  10. V. Girault and J.L. Lions, Two-grid finite-element schemes for the transient Navier–Stokes problem. ESAIM: M2AN 35 (2001) 945–980. [CrossRef] [EDP Sciences] [Google Scholar]
  11. V. Girault and P.A. Raviart. Finite element methods for Navier–Stokes equations: theory and algorithms. Springer-Verlag, Berlin (1986). [Google Scholar]
  12. F. Guillén-González and J.V. Gutiérrez-Santacreu, Unconditional stability and convergence of a fully discrete scheme for 2D viscous fluids models with mass diffusion. Math. Comput. 77 (2008) 1495–1524. [CrossRef] [MathSciNet] [Google Scholar]
  13. F.H. Lin, Nonlinear theory of defects in nematic liquid crystals: phase transition and flow phenomena. Comm. Pure Appl. Math. 42 (1989) 789–814. [CrossRef] [Google Scholar]
  14. F.H. Lin and C. Liu, Non-parabolic dissipative systems modelling the flow of liquid crystals. Comm. Pure Appl. Math. 48 (1995) 501–537. [CrossRef] [Google Scholar]
  15. F. H. Lin and C. Liu, Existence of solutions for the Ericksen–Leslie system. Arch. Rational. Mech. Anal. 154 (2000) 135–156. [CrossRef] [Google Scholar]
  16. P. Lin and C. Liu, Simulations of singularity dynamics in liquid crystal flows: A C0 finite element approach. J. Comput. Phys. 215 (2006) 1411–1427. [Google Scholar]
  17. P. Lin, C. Liu and H. Zhang, An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal flow dynamics. J. Comput. Phys. 227 (2007) 348–362. [Google Scholar]
  18. C. Liu and N.J. Walkington, Approximation of liquid crystal flows. SIAM J. Numer. Anal. 37 (2000) 725–741. [CrossRef] [MathSciNet] [Google Scholar]
  19. 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]
  20. A.J. Majda and A.L. Bertozzi, Vorticity and incompressible flows. Cambridge Texts in Applied Mathematics (2002). [Google Scholar]
  21. L. R. Scott and S. Zhang, Finite element interpolation of non-smooth functions satisfying boundary conditions. Math. Comput. 54 (1990) 483–493. [Google Scholar]
  22. J. Shen and X. Yang, Numerical approximations of Allen-Cahn and Cahn-Hilliard equations. Discrete Cont. Dyn. Sys. 28 (2010) 1669–1691. [Google Scholar]
  23. J. Simon, Compact sets in the Space Lp(0,T;B). Ann. Mat. Pura Appl. 146 (1987) 65–97. [Google Scholar]

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