Behavior of Lagrange-Galerkin solutions to the Navier-Stokes problem for small time increment

被引：0

作者：

Tabata, Masahisa ^{[1
]}

Uchiumi, Shinya ^{[2
,3
]}

机构：

[1] Kyushu Univ, Fac Math, Fukuoka, Japan

[2] Gakushuin Univ, Dept Math, Toshima, Japan

[3] Gakushuin Univ, Dept Math, Tokyo 1718588, Japan

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 39卷 / 06期

基金：

日本学术振兴会;

关键词：

Lagrange-Galerkin scheme; Navier-Stokes equations; numerical quadrature; QUADRATURE-FORMULAS; APPROXIMATION; CONVERGENCE; STABILITY; EQUATIONS; SCHEME; FLOW;

D O I：

10.1002/num.23051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider two kinds of numerical quadrature formulas of Gauss type and Newton-Cotes type, which are required in the real computation of Lagrange-Galerkin scheme for the Navier-Stokes problem. The Lagrange-Galerkin scheme with numerical quadrature, which has been used practically but not fully analyzed, is proved to be convergent at least for Gauss type quadrature under a condition on the time increment. As for the scheme with Newton-Cotes type quadrature, it has more smooth convergent property than that of Gauss type, whose reason is discussed.

引用

页码：4295 / 4316

页数：22

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