Discontinuous Galerkin finite element methods for the Landau-de Gennes minimization problem of liquid crystals
Maity, Ruma Rani and Majumdar, Apala and Nataraj, Neela (2020) Discontinuous Galerkin finite element methods for the Landau-de Gennes minimization problem of liquid crystals. IMA Journal of Numerical Analysis. ISSN 0272-4979 (In Press)
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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.
Creators(s): |
Maity, Ruma Rani, Majumdar, Apala ![]() | Item type: | Article |
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ID code: | 71536 |
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: | 25 Feb 2021 01:32 |
Related URLs: | |
URI: | https://strathprints.strath.ac.uk/id/eprint/71536 |
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