An A Posteriori Error Estimator for Electrically Coupled Liquid Crystal Equilibrium Configurations
This provides a more efficient computational method for simulating liquid crystal systems, which is incremental but important for materials science and engineering applications.
The paper tackles the problem of accurately simulating electrically coupled liquid crystal configurations by deriving an a posteriori error estimator for a nonlinear model, with numerical experiments showing significant efficiency improvements through adaptive refinement.
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.