An A Posteriori Error Estimator for Electrically Coupled Liquid Crystal Equilibrium Configurations

Abstract

This paper derives an a posteriori error estimator for the nonlinear first-order optimality conditions associated with the electrically and flexoelectrically coupled Frank-Oseen model of liquid crystals, building on previous results for elastic systems. The estimator is proposed for a penalty approach to imposing the unit-length constraint required by the model. Moreover, theory is proven establishing that the estimator provides a reliable estimate of global approximation error and an efficient measure of local error, suitable for use in adaptive refinement. Numerical experiments demonstrate significant improvements in efficiency with adaptive refinement guided by the proposed estimator in a multilevel, nested-iteration framework and superior physical properties for challenging electrically coupled systems.