Within this article, we develop a residual type a posteriori error estimator for a time discrete quasi-static phase-field fracture model. Particular emphasize is given to the robustness of the error estimator for the variational inequality governing the phase-field evolution with respect to the phase-field regularization parameter $\epsilon$. The article concludes with numerical examples highlighting the performance of the proposed a posteriori error estimators on three standard test cases; the single edge notched tension and shear test as well as the L-shaped panel test.

翻译：在本篇文章中,我们开发了一种剩余类型的后置误差估计器,用于一个时间离散的准静态相位断裂模型,特别强调了在阶段-现场规范参数($\epsilon$)方面,关于阶段-场演变变化变化的误差估计器的稳健性。文章最后用数字例子强调了三个标准测试案例中拟议的后置误测器的性能;单一边缘结扎的紧张度和剪切试验以及L形面板试验。