Uniform Error Estimates of the Finite Element Method for the Navier-Stokes Equations in R2 with L2 Initial Data

被引：0

作者：

Ren, Shuyan ^{[1
]}

Wang, Kun ^{[2
]}

Feng, Xinlong ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China

[2] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

来源：

ENTROPY | 2023年 / 25卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Navier-Stokes equations; finite element method; uniform error estimate; L-2 initial data; GALERKIN METHOD; SMOOTHING PROPERTY; STABILITY; APPROXIMATION; SCHEME;

D O I：

10.3390/e25050726

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we study the finite element method of the Navier-Stokes equations with the initial data belonging to the L-2 space for all time t > 0. Due to the poor smoothness of the initial data, the solution of the problem is singular, although in the H-1-norm, when t is an element of [0, 1). Under the uniqueness condition, by applying the integral technique and the estimates in the negative norm, we deduce the uniform-in-time optimal error bounds for the velocity in H-1-norm and the pressure in L-2-norm.

引用

页数：20

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