Free access
Issue
ESAIM: M2AN
Volume 36, Number 2, March/April 2002
Page(s) 205 - 222
DOI http://dx.doi.org/10.1051/m2an:2002010
Published online 15 May 2002
  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]
  2. F. Alouges and J.M. Ghidaglia, Minimizing Oseen-Frank energy for nematic liquid crystals: algorithms and numerical results. Ann. Inst. H. Poincaré Phys. Théor. 66 (1997) 411-447. [MathSciNet]
  3. I. Babuska and A.K. Aziz, Survey lecutures on the mathematical foundations of the finite element method, in The mathematical foundations of the finite element method with applications to partial differential equations, A.K. Aziz Ed., New York (1972), Academic Press, 5-359.
  4. F. Bethuel and H. Brezis, Regularity of minimizers of relaxed problems for harmonic maps. J. Funct. Anal. 101 (1991) 145-161. [CrossRef] [MathSciNet]
  5. F. Bethuel, H. Brezis and F. Helein, Ginzburg-Landau Vorticies. Klumer (1995).
  6. H. Brezis, New developments on the ginzburg-landau model. Topol. Methods Nonlinear Anal. 4 (1994) 227-236. [MathSciNet]
  7. H. Brezis, J. Coron and E. Lieb, Harmonic maps with defects. Comm. Math. Phys. 107 (1986) 649-705. [CrossRef] [MathSciNet]
  8. F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, no. 15 in Computational Mathematics. Springer-Verlag (1991).
  9. S. Chandrasekhar, Liquid Crystals. Cambridge (1992).
  10. Y.M. Chen and M. Struwe, Regularity for heat flow for harmonic maps. Math. Z. 201 (1989) 83-103. [CrossRef] [MathSciNet]
  11. P.G. Ciarlet, The finite element method for elliptic problems. North-Holland (1978).
  12. 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., Vol. 5 of The IMA Volumes in Mathematics and its Applicatoins. Springer-Verlag, New York (1987).
  13. R. Cohen, S. Lin and M. Luskin, Relaxation and gradient methods for molecular orientation in liquid crystals. Comp. Phys. 53 (1989) 455-465.
  14. M. Crouzeix and V. Thomee, The stability in Lp and W1,p of the L2 projection onto finite element function spaces. Math. Comp. 48 (1987) 521-532. [MathSciNet]
  15. T. Davis and E. Gartland, Finite element analsyis of the Landau-De Gennes minimization problem for liquid crystals. SIAM J. Numer. Anal. 35 (1998) 336-362. [CrossRef] [MathSciNet]
  16. P.G. de Gennes, The Physics Of Liquid Crystals. Oxford (1974).
  17. J. Deang, Q. Du, M. Gunzburger and J. Peterson, Vortices in superconductors: modelling and computer simulations. Philos. Trans. Roy. Soc. London 355 (1997) 1957-1968. [CrossRef] [MathSciNet]
  18. Q. Du and F. Lin, Ginzburg-Landau vortices: dynamics, pinning, and hysteresis. SIAM J. Math. Anal. 28 (1997) 1265-1293. [CrossRef] [MathSciNet]
  19. Q. Du, R.A. Nicolaides and X. Wu, Analysis and convergence of a covolume approximation of the Ginzburg-Landau model of superconductivity. SIAM J. Numer. Anal. 35 (1997) 1049-1072. [CrossRef]
  20. J. Ericksen, Conservation laws for liquid crystals. Trans. Soc. Rheol. 5 (1961) 22-34.
  21. F.C. Frank, On the theory of liquid crystals. Discuss. Faraday Soc. 28 (1958) 19-28. [CrossRef]
  22. V. Girault and P.A. Raviart, Finite element approximation of the Navier-Stokes equations, no. 749 in Lecture Notes in Mathematics. Springer Verlag, Berlin, Heidelbert, New York (1979).
  23. M. E. Gurtin, An introduction to continuum mechanics, no. 158 in Mathematics in Science and Engineering. Academic Press (1981).
  24. 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., Vol. 5 of The IMA Volumes in Mathematics and its Applicatoins. Springer-Verlag, New York (1987).
  25. R. Hardt, D. Kinderlehrer and F.H. Lin, Existence and partial regularity of static liquid crystal configurations. Comm. Math. Phys. 105 (1986) 547-570. [CrossRef] [MathSciNet]
  26. R. Hardt and F.H. Lin, Stability of singularities of minimizing harmonic maps. J. Differential Geom. 29 (1989) 113-123. [MathSciNet]
  27. R. Jerard and M. Soner, Dynamics of Ginzburg-Landau vortices. Arch. Rational Mech. Anal. 142 (1998) 99-125. [CrossRef] [MathSciNet]
  28. J. Jost, Harmonic mapping between Riemannian surfaces. Vol. 14 of Proc. of the C.M.A., Australian National University (1983).
  29. F. Leslie, Some constitutive equations for liquid crystals. Archive for Rational Mechanics and Analysis 28 (1968) 265-283. [MathSciNet]
  30. F. Leslie, Some topics in equilibrium theory of liquid crystals, in Theory and Applications of Liquid Crystals, J.L. Ericksen and D. Kinderlehrer Eds., Vol. 5 of The IMA Volumes in Mathematics and its Applications. Springer-Verlag, New York (1987) 211-234.
  31. 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).
  32. F.H. Lin, Some dynamic properties of Ginzburg-Landau vorticies. Comm. Pure Appl. Math. 49 (1996) 323-359. [CrossRef] [MathSciNet]
  33. F.H. Lin and C. Liu, Nonparabolic dissipative systems, modeling the flow of liquid crystals. Comm. Pure Appl. Math. XLVIII (1995) 501-537.
  34. F.H. Lin and C. Liu, Global existence of solutions for the Ericksen Leslie-system. Arch. Rational Mech. Anal. (1998).
  35. S. Lin and M. Luskin, Relaxation methods for liquid crystal problems. SIAM J. Numer. Anal. 26 (1989) 1310-1324. [CrossRef] [MathSciNet]
  36. C. Liu, Dynamic theory for incompressible smectic-A liquid crystals: Existence and regularity. Discrete Contin. Dynam. Systems 6 (2000) 591-608. [CrossRef] [MathSciNet]
  37. C. Liu and N.J. Walkington, Approximation of liquid crystal flows. SIAM J. Numer. Anal. 37 (2000) 725-741. [CrossRef] [MathSciNet]
  38. C.W. Oseen, The theory of liquid crystals. Trans. Faraday Soc. 29 (1933) 883-889. [CrossRef]
  39. R. Rannacher and R. Scott, Some optimal error estimates for piecewise linear finite element approximations. Math. Comp. 38 (1982) 437-445. [CrossRef] [MathSciNet]
  40. A.H. Schatz and L.B. Wahlbin, On the quasi-optimality in L of the H10 projection into finite element spaces. Math. Comp. 38 (1982) 1-22. [MathSciNet]
  41. R. Schoen and K. Uhlenbeck, A regularity theory for harmonic maps. J. Differential Geom. 17 (1982) 307-335. [MathSciNet]
  42. J. Shatah, Weak solutions and development of singularities in su(2) σ-model. CPAM 41 (1988) 459-469.
  43. R. Stenberg, On some three dimensional finite elements for incompressible materials. Comput. Methods Appl. Mech. Engrg. 63 (1987) 261-269. [CrossRef] [MathSciNet]
  44. R. Stenberg, Error analysis of some finite element methods for the Stokes problem. Math. Comp. 54 (1990) 495-508. [CrossRef] [MathSciNet]
  45. R. Temam, Navier-Stokes Equations. North Holland (1977).

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