Discontinuous Galerkin finite element methods for the Landau-de Gennes minimization problem of liquid crystals

Maity, Ruma Rani and Majumdar, Apala and Nataraj, Neela (2021) Discontinuous Galerkin finite element methods for the Landau-de Gennes minimization problem of liquid crystals. IMA Journal of Numerical Analysis, 41 (2). 1130–1163. ISSN 0272-4979 (https://doi.org/10.1093/imanum/draa008)

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Abstract

We consider a system of second order non-linear elliptic partial differential equations that models the equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin finite element methods are used to approximate the solutions of this nonlinear problem with non-homogeneous Dirichlet boundary conditions. A discrete inf-sup condition demonstrates the stability of the discontinuous Galerkin discretization of a well-posed linear problem. We then establish the existence and local uniqueness of the discrete solution of the non-linear problem. An a priori error estimates in the energy and L2 norm are derived and a best approximation property is demonstrated. Further, we prove the quadratic convergence of Newton’s iterates along with complementary numerical experiments.

ORCID iDs

Maity, Ruma Rani, Majumdar, Apala ORCID logoORCID: https://orcid.org/0000-0003-4802-6720 and Nataraj, Neela;
  • Item type:Article
    ID code:71536
    Dates:
    Date
    Event
    30 April 2021
    Published
    19 June 2020
    Published Online
    11 February 2020
    Accepted
    Keywords:nematic liquid crystals, energy optimization, Landau-de Gennes energy functional, discontinuous Galerkin finite element methods, error analysis, convergence rate, Mathematics, Mathematics(all)
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:24 Feb 2020 09:43
    Last modified:28 Mar 2023 10:21
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/71536
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