A nonconforming finite element method for the stationary Smagorinsky model
A nonconforming finite element method for the stationary Smagorinsky model
复制标题
平稳Smagorinsky模型的非协调有限元方法
DOI：
10.1016/j.amc.2019.02.012
复制
发表时间：
2019
影响因子：
4
通讯作者：
Li Zhenzhen
中科院分区：
文献类型：
--
作者：
Shi Dongyang;Li Minghao;Li Zhenzhen
本文主要研究定常Smagorinsky模型的一种低阶非线性有限元方法。速度和压力分别用约束二次旋转Q1元（CN Q1 r ot）和分段常数元逼近。利用非线性分析技巧和Aubin-Nitsche对偶性论证，推导出速度在破H1模和破L2模下的最优误差估计以及压力在破L2模下的最优误差估计。在一些合理的正则性假设下，也得到了超逼近和超收敛的结果。最后，通过数值算例验证了理论分析的正确性.
In this paper, we focus on a low order nonconforming finite element method (FEM) for the stationary Smagorinsky model. The velocity and pressure are approximated by the constrained nonconforming rotated Q 1 element (CN Q 1 r o t) and piecewise constant element, respectively. Optimal error estimates of the velocity in the broken H 1-norm and L 2-norm, and the pressure in the L 2-norm are derived by some nonlinear analysis techniques and Aubin-Nitsche duality argument. The supercloseness and superconvergent results are also obtained under some reasonable regularity assumptions. Finally, a numerical example is implemented to confirm our theoretical analysis.