2019/07/31 by Ruma Rani Maity, Apala Majumdar, Neela Nataraj · 1 citation
Mathematics · Computer Science · #math.NA #cs.NA #msc:65N30 #msc:35J60 #msc:35J15
published as IMA Journal of Numerical Analysis, 2020 · 27 pages, 23 figures
arxiv created 2020/05/28 · arxiv updated 2020/05/29
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 estimate in the energy norm is derived and a best approximation property is demonstrated. Further, we prove the quadratic convergence of Newton's iterates along with complementary numerical experiments.