An Error Estimator for Electrically Coupled Liquid Crystals

This paper extends an a posteriori error estimator for the elastic, Frank-Oseen model of liquid crystals, derived in [9], to include electric and flexoelectric effects. The problem involves a nonlinear coupled system of equations with a local unit-length constraint imposed via a penalty method. The proposed estimator is proven to be a reliable estimate of global approximation error. The performance of the coupled error estimator as a guide for adaptive refinement is shown in the numerical results, where the adapted grids successfully yield substantial reductions in computational work and comparable or better conformance to important physical laws.
Comment: 10 Pages, 2 Figures, Conference: LSSC 2023. arXiv admin note: substantial text overlap with arXiv:1806.06248