A comparison of three kinds of local and parallel finite element algorithms based on two-grid discretizations for the stationary Navier–Stokes equations
A comparison of three kinds of local and parallel finite element algorithms based on two-grid discretizations for the stationary Navier–Stokes equations
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DOI：
10.1016/j.compfluid.2010.09.009
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发表时间：
2011
影响因子：
2.8
通讯作者：
Yueqiang Shang;Yinnian He;Zhendong Luo
中科院分区：
文献类型：
--
作者：
Yueqiang Shang;Yinnian He;Zhendong Luo
基于两网格离散，介绍并讨论了三种求解平稳Navier-Stokes方程的局部和并行有限元算法。主要技术是首先在粗网格上使用标准有限元离散化来近似解的低频，然后在细网格上应用一些线性化离散化，通过一些局部和并行程序来校正结果残差（其中大部分包含高频）。讨论了三种线性化的方法。在唯一性条件下，导出了有限元解的误差估计。数值结果表明，在三种并行算法中，从计算时间和近似解精度两方面考虑，oseen -线性化算法是较好的并行算法。
Based on two-grid discretizations, three kinds of local and parallel finite element algorithms for the stationary Navier–Stokes equations are introduced and discussed. The main technique is first to use a standard finite element discretization on a coarse grid to approximate low frequencies of the solution, then to apply some linearized discretizations on a fine grid to correct the resulted residual (which contains mostly high frequencies) by some local and parallel procedures. Three approaches to linearization are discussed. Under the uniqueness condition, error estimates of the finite element solution are derived. Numerical results show that among the three kinds of parallel algorithms, the Oseen-linearized algorithm is preferable if we both consider the computational time and the accuracy of the approximate solution.