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:在这项工作中,我们开发了一种在线适应性浓缩方法,在限制能源以尽量减少普遍规模多功能元件法(CEM-GMSFEM)的框架内,解决线性异质多孔弹性模型,其系数差异很大。拟议方法利用残余驱动误差指标的信息来丰富模型中移位和压力变量的多尺度空间。更多的在线基础功能也相应地在过度抽样的区域建立,并经过适应性选择,以尽量减少误差。对在线浓缩算法进行了全面的理论分析,并通过彻底的数值实验加以证明。