Finite element analysis of the landau-de gennes minimization problem for liquid crystals

Abstract

This paper describes the Landau-de Gennes free-energy minimization problem for computing equilibrium configurations of the tensor order parameter field that characterizes the molecular orientational properties of liquid crystal materials. Analytical and numerical issues are addressed. Conditions guaranteeing well-posedness (existence, regularity) of the problem are given, as is a nonlinear finite element convergence analysis.