Maity, Ruma Rani ; Majumdar, Apala ; Nataraj, Neela (2020) Discontinuous Galerkin finite element methods for the Landau–de Gennes minimization problem of liquid crystals IMA Journal of Numerical Analysis, 41 (2). pp. 1130-1163. ISSN 0272-4979
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Official URL: http://doi.org/10.1093/imanum/draa008
Related URL: http://dx.doi.org/10.1093/imanum/draa008
Abstract
We consider a system of second-order nonlinear elliptic partial differential equations that models the equilibrium configurations of a two-dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin (dG) finite element methods are used to approximate the solutions of this nonlinear problem with nonhomogeneous Dirichlet boundary conditions. A discrete inf–sup condition demonstrates the stability of the dG discretization of a well-posed linear problem. We then establish the existence and local uniqueness of the discrete solution of the nonlinear problem. A priori error estimates in the energy and L2 norms are derived and a best approximation property is demonstrated. Further, we prove the quadratic convergence of the Newton iterates along with complementary numerical experiments.
Item Type: | Article |
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Source: | Copyright of this article belongs to Oxford University Press. |
ID Code: | 122900 |
Deposited On: | 26 Aug 2021 05:49 |
Last Modified: | 26 Aug 2021 05:49 |
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