Fast Online Adaptive Enrichment for Poroelasticity with High Contrast

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.