Investigations on two kinds of two-level stabilized finite element methods for the stationary Navier-Stokes equations
Investigations on two kinds of two-level stabilized finite element methods for the stationary Navier-Stokes equations
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平稳Navier-Stokes方程的两种两级稳定有限元方法研究
DOI：
10.1016/j.amc.2006.05.034
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发表时间：
2006-11-15
影响因子：
4
通讯作者：
Li, Jian
中科院分区：
文献类型：
--
作者：
Li, Jian
考虑了用不满足inf-sup条件的最低等阶元逼近二维定常Navier-Stokes方程的两种基于局部Gauss积分技术的两层稳定化有限元方法。两级方法包括在粗网格上求解一个小的非线性系统，然后在细网格上求解一个线性系统。误差分析表明，在适当选取网格宽度的情况下，两层稳定化有限元法可提供与通常的稳定化有限元法在细网格上求解Navier-Stokes方程时相同阶收敛速度的近似解。因此，两层方法在科学计算中具有重要的实际意义。最后，通过一系列的数值实验，从效率和精度两个方面比较了两种两级稳定化方法的性能。结论是简单的两层稳定化方法是求解定常Navier-Stokes问题最低等阶近似的一种可行的选择。(c)2006年爱思唯尔公司All rights reserved.
This article considers two kinds of two-level stabilized finite element methods based on local Gauss integral technique for the two-dimensional stationary Navier-Stokes equations approximated by the lowest equal-order elements which do not satisfy the inf-sup condition. The two-level methods consist of solving a small non-linear system on the coarse mesh and then solving a linear system on the fine mesh. The error analysis shows that the two-level stabilized finite element methods provide an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution solving the Navier-Stokes equations on a fine mesh for a related choice of mesh widths. Therefore, the two-level methods are of practical importance in scientific computation. Finally, the performance of two kinds of two-level stabilized methods are compared in efficiency and precision aspects by a series of numerical experiments. The conclusion is that simple two-level stabilized method is a viable choice for the lowest equal-order approximations of the stationary Navier-Stokes problem. (c) 2006 Elsevier Inc. All rights reserved.