Stabilized mixed finite element methods for the Navier-Stokes equations with damping

被引：18

作者：

Li, Zhenzhen ^{[1
]}

Shi, Dongyang ^{[2
]}

Li, Minghao ^{[3
]}

机构：

[1] Zhengzhou Univ Light Ind, Coll Math & Informat Sci, Zhengzhou, Henan, Peoples R China

[2] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China

[3] Henan Univ Technol, Coll Sci, Zhengzhou, Henan, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2019年 / 42卷 / 02期

关键词：

Navier-Stokes equations with damping; optimal error estimates; stabilization; two-step method; EFFICIENT 2-STEP ALGORITHM; 2-GRID METHOD; 2-LEVEL DISCRETIZATION; CONVERGENCE; EXISTENCE; SCHEME; WEAK;

D O I：

10.1002/mma.5365

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 the H-1-norm and L-2-norm of the velocity and the L-2-norm of the pressure are derived. Moreover, on the basis of the optimal L-2-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.

引用

页码：605 / 619

页数：15

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