On local conservation of numerical methods for conservation laws

被引：14
|
作者：
Shi, Cengke [1 ]
Shu, Chi-Wang [1 ]
机构：
[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA
来源：
COMPUTERS & FLUIDS | 2018年 / 169卷
基金：
美国国家科学基金会;
关键词：
Local conservation property; Conservation laws; Lax-Wendroff theorem; Compact schemes; Continuous finite element Galerkin method; FINITE-ELEMENT-METHOD; SCHEMES;
D O I：
10.1016/j.compfluid.2017.06.018
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this paper we introduce a definition of the local conservation property for numerical methods solving time dependent conservation laws, which generalizes the classical local conservation definition. The motivation of our definition is the Lax-Wendroff theorem, and thus we prove it for locally conservative numerical schemes per our definition in one and two space dimensions. Several numerical methods, including continuous Galerkin methods and compact schemes, which do not fit the classical local conservation definition, are given as examples of locally conservative methods under our generalized definition. (C) 2017 Elsevier Ltd. All rights reserved.
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页码：3 / 9
页数：7
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