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

在本文中，我们考虑了多孔区域中不可压缩的斯托克斯流问题，并采用约束能量最小化的广义多尺度有限元方法（CEM-GMsFEM）解决了该问题。所提出的方法提供了一种灵活且系统的方法来构造关键的无散度的多尺度基函数，以近似速度场。这些基本函数是通过解决本征空间中包含异质性局部信息的一类局部能量最小化问题而构造的。这些多尺度基函数显示为在相应的局部过采样区域之外具有指数衰减的特性。通过采用过采样技术，证明了该方法具有误差范围与粗糙网格尺寸有关的谱收敛性。