  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.
