论文标题
可扩展的本地和平行的两网格有限元方案
Expandable Local and Parallel Two-Grid Finite Element Scheme for the Stokes Equations
论文作者
论文摘要
在本文中，我们提出了一种新型的本地和平行的两网格有限元方案，用于求解Stokes方程，并严格建立其先验误差估计。该方案同时承认了子域及其扩展之间的子问题和距离的小尺度，因此可以扩展。基于先验误差估计，我们提供了具有合适迭代编号的相应迭代方案。如果粗网格尺寸$ h $，并且正确选择了$ O（| \ ln H |）$（3-d中的$ O（| \ ln H |^2）$，则可以在3-D中$ O（| \ ln H |）$（3-D）中的最佳收敛订单（如果粗网格尺寸$ h $，并且正确选择了罚款$ h $），则可以在2-D和$ O（| \ ln H |）中达到最佳收敛订单。最后，进行了一些数值测试，包括2-D和3-D病例，以验证我们的理论结果。
In this paper, we present a novel local and parallel two-grid finite element scheme for solving the Stokes equations, and rigorously establish its a priori error estimates. The scheme admits simultaneously small scales of subproblems and distances between subdomains and its expansions, and hence can be expandable. Based on the a priori error estimates, we provide a corresponding iterative scheme with suitable iteration number. The resulting iterative scheme can reach the optimal convergence orders within specific two-grid iterations ($O(|\ln H|^2)$ in 2-D and $O(|\ln H|)$ in 3-D) if the coarse mesh size $H$ and the fine mesh size $h$ are properly chosen. Finally, some numerical tests including 2-D and 3-D cases are carried out to verify our theoretical results.
