Before revision: The equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device are modelled by a system of second order semi-linear elliptic partial differential equations with non-homogeneous boundary conditions. In this article, Nitsche's method is applied to approximate the solution of this non-linear model.
After revision: The equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device are modelled by a system of second order semi-linear elliptic partial differential equations with a lower order cubic nonlinear term, and inhomogeneous Dirichlet boundary conditions, relevant for two-dimensional bistable liquid crystal devices, within a reduced Landau-de Gennes framework. The main results are (i) a priori error estimates for the energy norm and the L^2 norm, within the Nitsche's method is applied to approximate the solution of this non-linear model.