In this work, we develop an online adaptive enrichment method within the framework of the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving the linear heterogeneous poroelasticity models with coefficients of high contrast. The proposed method makes use of information of residual-driven error indicators to enrich the multiscale spaces for both the displacement and the pressure variables in the model. Additional online basis functions are constructed in oversampled regions accordingly and are adaptively chosen to reduce the error the most. A complete theoretical analysis of the online enrichment algorithm is provided and justified by thorough numerical experiments.

翻译：本文在约束能量最小化广义多尺度有限元方法（CEM-GMsFEM）框架内，针对具有高对比度系数的线性非均质孔隙弹性模型，提出了一种在线自适应富集方法。该方法利用残差驱动误差指示器的信息，对模型中位移变量和压力变量的多尺度空间进行富集。根据误差指示器在过采样区域构造额外的在线基函数，并自适应地选择这些基函数以最大程度地降低误差。本文提供了在线富集算法的完整理论分析，并通过详尽的数值实验加以验证。