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. A discrete inf-sup condition sufficient for the stability of a well-posed linear problem is established and this with a fixed point theorem allows the proof of local existence and uniqueness of a discrete solution to the semi-linear problems.%DIFDELCMD < {\it %%% A priori and  {\it a posteriori} energy norm analysis is established for a sufficiently large penalization parameter and  sufficiently fine triangulation . Optimal order%DIFDELCMD < {\it %%% a priori error estimates in L^2 norm is also established. Several numerical examples that confirm the theoretical results are presented .
We study a system of 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 %DIFDELCMD < {\it %%% and discontinuous Galerkin frameworks under milder regularity assumptions on the exact solution and (ii) a reliable and efficient {\it a posteriori} analysis for a sufficiently large penalization parameter and a sufficiently fine triangulation %DIFDELCMD < {\it %%% in both cases. Numerical examples that validate the theoretical results , are presented separately .
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The equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device are modelled by a system of second order
We study a system of
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non-homogeneous boundary conditions. In this article,
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
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method is applied to approximate the solution of this non-linear model. A discrete inf-sup condition sufficient for the stability of a well-posed linear problem is established and this with a fixed point theorem allows the proof of local existence and uniqueness of a discrete solution to the semi-linear problems.
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and discontinuous Galerkin frameworks under milder regularity assumptions on the exact solution
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(ii) a reliable and efficient
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energy norm analysis is established
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error estimates in L^2 norm is also established. Several numerical examples that confirm
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