Suitable weak solutions of the Navier-Stokes equations constructed by a space-time numerical discretization

被引：5

作者：

Berselli, Luigi C. ^{[1
]}

Fagioli, Simone ^{[2
]}

Spirito, Stefano ^{[2
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, Via F Buonarroti 1-C, I-56127 Pisa, Italy

[2] Univ Aquila, DISIM, Via Vetoio, I-67100 Laquila, Italy

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2019年 / 125卷

关键词：

Navier-Stokes equations; Local energy inequality; Numerical schemes; theta-method; Finite element and finite difference methods; SLIP BOUNDARY-CONDITIONS; SEMI-DISCRETIZATION; PARTIAL REGULARITY;

D O I：

10.1016/j.matpur.2018.09.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that weak solutions obtained as limits of certain numerical space-time discretizations are suitable in the sense of Scheffer and Caffarelli-Kohn-Nirenberg. More precisely, in the space-periodic setting, we consider a full discretization in which the theta-method is used to discretize the time variable, while in the space variables we consider appropriate families of finite elements. The main result is the validity of the so-called local energy inequality. (C) 2018 Elsevier Masson SAS. All rights reserved.

引用

页码：189 / 208

页数：20

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