An Error Estimator for Electrically Coupled Liquid Crystals

04/04/2023

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by   J. H. Adler, et al.

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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.