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

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Numerical Methods for Partial Differential Equations Pub Date : 2023-06-04 DOI:10.1002/num.23051

M. Tabata, Shinya Uchiumi

引用次数: 0

Abstract

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.

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小时间增量Navier-Stokes问题的Lagrange‐Galerkin解的性质

本文考虑了Navier-Stokes问题的Lagrange-Galerkin格式的实际计算中所需要的Gauss型和Newton‐Cotes型两种数值正交公式。具有数值正交的拉格朗日-伽辽金格式在一定的时间增量条件下，至少对高斯型正交是收敛的。对于具有Newton - Cotes型正交的格式，它具有比高斯型格式更光滑的收敛性，并讨论了其原因。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Methods for Partial Differential Equations 数学-应用数学

CiteScore

7.20

自引率

2.60%

发文量

审稿时长

9 months

期刊介绍： An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.