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Volumn 35, Issue 1, 1998, Pages 336-362

Finite element analysis of the landau-de gennes minimization problem for liquid crystals

Author keywords

Finite elements; Landau de gennes free energy; Liquid crystals; Nonlinear convergence analysis

Indexed keywords


EID: 0000484868     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142996297448     Document Type: Article
Times cited : (105)

References (49)
  • 1
    • 0003362526 scopus 로고
    • Sobolev Spaces
    • Academic Press, Orlando, FL
    • R. A. ADAMS, Sobolev Spaces, Pure and Applied Mathematics 65, Academic Press, Orlando, FL, 1975.
    • (1975) Pure and Applied Mathematics , vol.65
    • Adams, R.A.1
  • 2
    • 84980075953 scopus 로고
    • Estimates near the boundary for the solutions of elliptic differential equations satisfying general boundary values I
    • S. AGMON, A. DOUGLIS, AND L. NIRENBERG, Estimates near the boundary for the solutions of elliptic differential equations satisfying general boundary values I, Comm. Pure Appl. Math., 12 (1959), pp. 623-727.
    • (1959) Comm. Pure Appl. Math. , vol.12 , pp. 623-727
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 3
    • 84980080664 scopus 로고
    • Estimates near the boundary for the solutions of elliptic differential equations satisfying general boundary values II
    • S. AGMON, A. DOUGLIS, AND L. NIRENBERG, Estimates near the boundary for the solutions of elliptic differential equations satisfying general boundary values II, Comm. Pure Appl. Math., 17 (1964), pp. 35-92.
    • (1964) Comm. Pure Appl. Math. , vol.17 , pp. 35-92
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 6
    • 0003947266 scopus 로고
    • Applied Functional Analysis
    • John Wiley, New York
    • J.-P. AUBIN, Applied Functional Analysis, Pure and Applied Mathematics, John Wiley, New York, 1979.
    • (1979) Pure and Applied Mathematics
    • Aubin, J.-P.1
  • 8
    • 0000667167 scopus 로고
    • Tensor representation of Oseen-Frank strain energy in uniaxial cholesterics
    • D. W. BERREMAN AND S. MEIBOOM, Tensor representation of Oseen-Frank strain energy in uniaxial cholesterics, Phys. Rev. A, 30 (1984), pp. 1955-1959.
    • (1984) Phys. Rev. A , vol.30 , pp. 1955-1959
    • Berreman, D.W.1    Meiboom, S.2
  • 9
    • 0002435262 scopus 로고
    • Finite dimensional approximation of nonlinear problems. Part I: Branches of nonsingular solutions
    • F. BREZZI, J. RAPPAZ, AND P. A. RAVIART, Finite dimensional approximation of nonlinear problems. Part I: Branches of nonsingular solutions, Numer. Math., 36 (1980), pp. 1-25.
    • (1980) Numer. Math. , vol.36 , pp. 1-25
    • Brezzi, F.1    Rappaz, J.2    Raviart, P.A.3
  • 13
    • 0002214863 scopus 로고
    • Minimum energy configurations for liquid crystals: Computational results
    • J. L. Ericksen and D. Kinderlehrer, eds., IMA Volumes in Mathematics and its Applications 5, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo
    • 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., IMA Volumes in Mathematics and its Applications 5, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo, 1987, pp. 400-408.
    • (1987) Theory and Applications of Liquid Crystals , pp. 400-408
    • Cohen, R.1    Hardt, R.2    Kinderlehrer, D.3    Lin, S.4    Luskin, M.5
  • 16
    • 0015018982 scopus 로고
    • Short range order effects in the isotropic phase of nematics and cholesterics
    • P. G. DE GENNES, Short range order effects in the isotropic phase of nematics and cholesterics, Mol. Cryst. Liq. Cryst., 12 (1971), pp. 193-214.
    • (1971) Mol. Cryst. Liq. Cryst. , vol.12 , pp. 193-214
    • De Gennes, P.G.1
  • 18
    • 0026838281 scopus 로고
    • Analysis and approximation of the Ginzburg-Landau model of superconductivity
    • Q. Du, M. D. GUNZBURGER, AND J. S. PETERSON, Analysis and approximation of the Ginzburg-Landau model of superconductivity, SIAM Rev., 34 (1992), pp. 54- 81.
    • (1992) SIAM Rev. , vol.34 , pp. 54-81
    • Du, Q.1    Gunzburger, M.D.2    Peterson, J.S.3
  • 19
    • 0026365370 scopus 로고
    • Liquid crystals with variable degree of orientation
    • J. L. ERICKSEN, Liquid crystals with variable degree of orientation, Arch. Rational Mech. Anal., 113 (1991), pp. 97-120.
    • (1991) Arch. Rational Mech. Anal. , vol.113 , pp. 97-120
    • Ericksen, J.L.1
  • 20
    • 0004599093 scopus 로고
    • On the discretization error of parametrized nonlinear equations
    • J. FINK AND W. RHEINBOLDT, On the discretization error of parametrized nonlinear equations, SIAM J. Numer. Anal., 20 (1983), pp. 732-746.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 732-746
    • Fink, J.1    Rheinboldt, W.2
  • 21
    • 0004623926 scopus 로고
    • Solution manifolds and submanifolds of parametrized equations and their discretization errors
    • J. FINK AND W. RHEINBOLDT, Solution manifolds and submanifolds of parametrized equations and their discretization errors, Numer. Math., 45 (1984), pp. 323-343.
    • (1984) Numer. Math. , vol.45 , pp. 323-343
    • Fink, J.1    Rheinboldt, W.2
  • 22
    • 0008820036 scopus 로고
    • On the theory of liquid crystals
    • F. C. FRANK, On the theory of liquid crystals, Discuss. Faraday Soc., 25 (1958), pp. 19-28.
    • (1958) Discuss. Faraday Soc. , vol.25 , pp. 19-28
    • Frank, F.C.1
  • 24
    • 0006986534 scopus 로고
    • Numerical minimization of the Landau-de Gennes free energy: Defects in cylindrical capillaries
    • E. C. GARTLAND, JR., P. PALFFY-MUHORAY, AND R. S. VARGA, Numerical minimization of the Landau-de Gennes free energy: Defects in cylindrical capillaries, Mol. Cryst. Liq. Cryst., 199 (1991), pp. 429-452.
    • (1991) Mol. Cryst. Liq. Cryst. , vol.199 , pp. 429-452
    • Gartland E.C., Jr.1    Palffy-Muhoray, P.2    Varga, R.S.3
  • 27
    • 0000415732 scopus 로고
    • Landau theory of the nematic-isotropic phase transition
    • E. F. GRAMSBERGEN, L. LONGA, AND W. H. DE JEU, Landau theory of the nematic-isotropic phase transition, Phys. Rev., 135 (1986), pp. 195-257.
    • (1986) Phys. Rev. , vol.135 , pp. 195-257
    • Gramsbergen, E.F.1    Longa, L.2    De Jeu, W.H.3
  • 30
    • 0000811335 scopus 로고
    • Mathematical questions of liquid crystal theory, in Theory and Applications of Liquid Crystals
    • J. L. Ericksen and D. Kinderlehrer, eds., Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo
    • 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., IMA Volumes in Mathematics and Its Applications 5, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo, 1987, pp. 151-184.
    • (1987) IMA Volumes in Mathematics and Its Applications , vol.5 , pp. 151-184
    • Hardt, R.1    Kinderlehrer, D.2
  • 31
    • 0000961863 scopus 로고
    • Existence and partial regularity of static liquid crystal configurations
    • R. HARDT, D. KINDERLEHRER, AND F.-H. LIN, Existence and partial regularity of static liquid crystal configurations, Comm. Math. Phys., 105 (1986), pp. 547-570.
    • (1986) Comm. Math. Phys. , vol.105 , pp. 547-570
    • Hardt, R.1    Kinderlehrer, D.2    Lin, F.-H.3
  • 32
    • 0029489948 scopus 로고
    • The approximation problem for drift-diffusion systems
    • J. W. JEROME, The approximation problem for drift-diffusion systems, SIAM Rev., 37 (1995), pp. 552-572.
    • (1995) SIAM Rev. , vol.37 , pp. 552-572
    • Jerome, J.W.1
  • 33
    • 0026139032 scopus 로고
    • A finite element approximation theory for the drift diffusion semiconductor model
    • J. W. JEROME AND T. KERKHOVEN, A finite element approximation theory for the drift diffusion semiconductor model, SIAM J. Numer. Anal., 28 (1991), pp. 403-422.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 403-422
    • Jerome, J.W.1    Kerkhoven, T.2
  • 36
    • 0003358572 scopus 로고
    • Relaxation methods for liquid crystal problems
    • S.-Y. LIN AND M. LUSKIN, Relaxation methods for liquid crystal problems, SIAM J. Numer. Anal., 26 (1989), pp. 1310-1324.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1310-1324
    • Lin, S.-Y.1    Luskin, M.2
  • 37
    • 0000441352 scopus 로고
    • An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals
    • L. LONGA, D. MONSELESAN, AND H. TREBIN, An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals, Liq. Crys., 2 (1987), pp. 769-796.
    • (1987) Liq. Crys. , vol.2 , pp. 769-796
    • Longa, L.1    Monselesan, D.2    Trebin, H.3
  • 41
    • 0003766467 scopus 로고
    • Finite Elements: Mathematical Aspects
    • Prentice-Hall, Englewood Cliffs, NJ
    • J. T. ODEN AND G. F. CAREY, Finite Elements: Mathematical Aspects, The Texas Finite Element Series IV, Prentice-Hall, Englewood Cliffs, NJ, 1983.
    • (1983) The Texas Finite Element Series , vol.4
    • Oden, J.T.1    Carey, G.F.2
  • 42
    • 37049160761 scopus 로고
    • The theory of liquid crystals
    • C. W. OSEEN, The theory of liquid crystals, Trans. Faraday Soc., 29 (1933), pp. 883-889.
    • (1933) Trans. Faraday Soc. , vol.29 , pp. 883-889
    • Oseen, C.W.1
  • 44
    • 33746299861 scopus 로고
    • Defect core structure in nematic liquid crystals
    • N. SCHOPOHL AND T. J. SLUCKIN, Defect core structure in nematic liquid crystals, Phys. Rev. Lett., 59 (1987), pp. 2582-2584.
    • (1987) Phys. Rev. Lett. , vol.59 , pp. 2582-2584
    • Schopohl, N.1    Sluckin, T.J.2
  • 45
  • 46
    • 0346960609 scopus 로고
    • The Landau Theory of Phase Transitions
    • World Scientific, Singapore, New Jersey, Hong Kong
    • J.-C. TOLÉDANO AND P. TOLÉDANO, The Landau Theory of Phase Transitions, Lecture Notes in Physics 3, World Scientific, Singapore, New Jersey, Hong Kong, 1987.
    • (1987) Lecture Notes in Physics , vol.3
    • Tolédano, J.-C.1    Tolédano, P.2
  • 47
    • 0012144309 scopus 로고
    • Functional Analysis and Approximation Theory in Numerical Analysis
    • SIAM, Philadelphia, PA
    • R. S. VARGA, Functional Analysis and Approximation Theory in Numerical Analysis, Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, PA, 1971.
    • (1971) Regional Conference Series in Applied Mathematics
    • Varga, R.S.1
  • 48
    • 0348106554 scopus 로고
    • Variational Theories for Liquid Crystals
    • Chapman and Hall, London, Glasgow, Weinheim, New York, Tokyo, Melbourne, Madras
    • E. G. VIRGA, Variational Theories for Liquid Crystals, Applied Mathematics and Mathematical Computation 8, Chapman and Hall, London, Glasgow, Weinheim, New York, Tokyo, Melbourne, Madras, 1994.
    • (1994) Applied Mathematics and Mathematical Computation , vol.8
    • Virga, E.G.1
  • 49
    • 37049177263 scopus 로고
    • The effect of a magnetic field on the nematic state
    • H. ZÖCHER, The effect of a magnetic field on the nematic state, Trans. Faraday Soc., 29 (1933), pp. 945-957.
    • (1933) Trans. Faraday Soc. , vol.29 , pp. 945-957
    • Zöcher, H.1


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