In this work, we derive a $\gamma$-robust a posteriori error estimator for finite element approximations of the Allen-Cahn equation with variable non-degenerate mobility. The estimator utilizes spectral estimates for the linearized steady part of the differential operator as well as a conditional stability estimate based on a weighted sum of Bregman distances, based on the energy and a functional related to the mobility. A suitable reconstruction of the numerical solution in the stability estimate leads to a fully computable estimator.

翻译：本文推导了变非退化流动性Allen-Cahn方程有限元近似的$\gamma$-鲁棒后验误差估计子。该估计子利用微分算子线性化稳态部分的谱估计，以及基于能量和流动性相关函数的Bregman距离加权和的条件稳定性估计。通过在稳定性估计中对数值解进行适当重构，得到了完全可计算的估计子。