A posteriori error estimates for Biot system using Enriched Galerkin for flow
A posteriori error estimates for Biot system using Enriched Galerkin for flow
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DOI：
10.1016/j.cma.2020.113185
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发表时间：
2020-09-01
影响因子：
7.2
通讯作者：
Wheeler, Mary F.
中科院分区：
文献类型：
--
作者：
Girault, Vivette;Lu, Xueying;Wheeler, Mary F.
我们分析了用固定应力分裂求解的Biot系统，流动方程的富伽辽金离散化，力学方程的伽辽金离散化。基于残差的后验误差估计建立了下界和上界。用曼德尔问题进行的数值实验证实了这些理论结果。通过一个包含裂缝网络的非常规油藏原型模型，验证了这些后验误差估计在指导动态网格细化方面的有效性。我们进一步提出了一种新的固定应力迭代停止准则，利用误差指标来平衡固定应力分裂误差和离散化误差。该停止准则不需要超参数调谐，在数值实验中证明了它的有效性和准确性。(C) 2020 Elsevier B.V.版权所有
We analyze the Biot system solved with a fixed-stress split, Enriched Galerkin (EG) discretization for the flow equation, and Galerkin for the mechanics equation. Residual-based a posteriori error estimates are established with both lower and upper bounds. These theoretical results are confirmed by numerical experiments performed with the Mandel's problem. The efficiency of these a posteriori error estimators to guide dynamic mesh refinement is demonstrated with a prototype unconventional reservoir model containing a fracture network. We further propose a novel stopping criterion for the fixed-stress iterations using the error indicators to balance the fixed-stress split error with the discretization errors. The new stopping criterion does not require hyperparameter tuning and demonstrates efficiency and accuracy in numerical experiments. (C) 2020 Elsevier B.V. All rights reserved.