In this work, we develop an online enrichment strategy within the framework of the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with coefficients of high contrast. The proposed method makes use of the fast online adaptive method to enrich the multiscale spaces for the displacement and the pressure. Additional online basis functions are computed in oversampled regions based on current residual information and are adaptively chosen to decrease the error the most. A complete theoretical analysis of the online enrichment algorithm is provided and justified by numerical experiments.

翻译：在这项工作中,我们在限制能源以尽量减少普遍规模多功能元素的方法(CEM-GMSFEM)的框架内,制定了在线浓缩战略,以解决线性多孔化问题,其系数差异很大。拟议方法采用快速在线适应方法,丰富多尺度的迁移空间和压力空间。基于现有残余信息,在过度抽样的区域计算了额外的在线基础功能,并适应性地选择了减少错误最多的功能。对在线浓缩算法进行了全面的理论分析,并以数字实验为根据。