In this article, we mainly propose and analyze a parallel stabilized finite element algorithm based upon two-grid discretization for the Navier-Stokes problem. The lowest equal-order finite element pairs are considered for the finite element discretization and a stabilized term based on two local Gauss integrations is introduced to circumvent the discrete inf-sup condition. The main idea is to utilize a partition of unity to assemble weighted local corrections of solutions on sub-domains. A further coarse grid correction is carried out to derive the optimal error estimates both in norm and norm. Theoretical results are rigorously established and some numerical experiments are reported to verify the theoretical results.

中文翻译：

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纳维-斯托克斯问题的并行稳定有限元方法


在本文中，我们主要针对Navier-Stokes问题提出并分析了一种基于二网格离散化的并行稳定有限元算法。有限元离散化考虑最低等阶有限元对，并引入基于两个局部高斯积分的稳定项来规避离散 inf-sup 条件。主要思想是利用统一划分来组合子域上解的加权局部校正。进行进一步的粗网格校正以获得范数和范数的最佳误差估计。严格建立了理论结果，并报告了一些数值实验来验证理论结果。