Convergence of the CEM-GMsFEM for Stokes flows in heterogeneous perforated domains

In this paper, we consider the incompressible Stokes flow problem in a perforated domain and employ constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to solve problem. The proposed provides flexible systematical approach construct crucial divergence-free basis functions for approximating velocity field. These are constructed by solving class of local minimization problems over eigenspaces that contain information on heterogeneities. shown have property exponential decay outside corresponding oversampling regions. By adopting technique oversampling, spectral convergence with error bounds related coarse mesh size is proved.