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.

翻译：本文将文献[9]中针对液晶弹性Frank-Oseen模型推导的后验误差估计器扩展至包含电效应和挠性电效应。该问题涉及一个非线性耦合方程组，并通过罚函数方法施加局部单位长度约束。所提出的估计器被证明能够可靠地估计全局逼近误差。数值结果表明，该耦合误差估计器作为自适应加密的指导，其性能表现优异：自适应网格成功实现了计算工作量的显著降低，并在关键物理规律的遵循程度上达到相当或更优的水平。