论文标题
CEM-GMSFEM在异质性穿孔域中流动的CEM-GMSFEM的收敛性
Convergence of the CEM-GMsFEM for Stokes flows in heterogeneous perforated domains
论文作者
论文摘要
在本文中，我们考虑了穿孔域中不可压缩的Stokes流量问题，并采用约束能量最大程度地减少通用多尺度有限元方法（CEM-GMSFEM）来解决此问题。所提出的方法提供了一种灵活而系统的方法来构建至关重要的多尺度基础函数，以近似位移场。这些基础函数是通过在包含有关异质性信息的本特征空间上解决一类局部能量最小化问题来构建的。这些多尺度函数显示出在相应的本地过采样区域之外具有指数衰减的属性。通过调整过采样的技术，可以证明该方法与与粗网格大小相关的误差界的光谱收敛。
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 displacement 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 adapting the technique of oversampling, the spectral convergence of the method with error bounds related to the coarse mesh size is proved.
