Stabilized mixed finite element methods for the Navier-Stokes equations with damping
Stabilized mixed finite element methods for the Navier-Stokes equations with damping
复制标题
带阻尼的纳维-斯托克斯方程的稳定混合有限元法
DOI：
10.1002/mma.5365
复制
发表时间：
2019
影响因子：
2.9
通讯作者：
Li Minghao
中科院分区：
文献类型：
--
作者：
Li Zhenzhen;Shi Dongyang;Li Minghao
本文给出了带阻尼项的Navier-Stokes方程的稳定化混合有限元方法。利用Brouwer不动点定理证明了弱解的存在唯一性。然后给出了速度的H1范数、L2范数和压力的L2范数的最优误差估计。此外，在速度最优L2范数误差估计的基础上，提出了一种比通常的稳定化方法更有效的稳定化两步法。最后，通过两个算例验证了理论分析的正确性。
In this paper, the stabilized mixed finite element methods are presented for the Navier‐Stokes equations with damping. The existence and uniqueness of the weak solutions are proven by use of the Brouwer fixed‐point theorem. Then, optimal error estimates for theH1‐norm andL2‐norm of the velocity and theL2‐norm of the pressure are derived. Moreover, on the basis of the optimalL2‐norm error estimate of the velocity, a stabilized two‐step method is proposed, which is more efficient than the usual stabilized methods. Finally, two numerical examples are implemented to confirm the theoretical analysis.