On the conservation and convergence to weak solutions of global schemes

被引：7

作者：

Carpenter, MH ^{[1
]}

Gottlieb, D

Shu, CW

机构：

[1] NASA, Langley Res Ctr, CMSB, Hampton, VA 23681 USA

[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2003年 / 18卷 / 01期

基金：

美国国家科学基金会; 美国国家航空航天局;

关键词：

conservation laws; conservation; weak solutions; convergence;

D O I：

10.1023/A:1020390212806

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we discuss the issue of conservation and convergence to weak solutions of several global schemes, including the commonly used compact schemes and spectral collocation schemes, for solving hyperbolic conservation laws. It is shown that such schemes, if convergent boundedly almost everywhere, will converge to weak solutions. The results are extensions of the classical Lax-Wendroff theorem concerning conservative schemes.

引用

页码：111 / 132

页数：22

共 21 条

[1]

Canuto C., 2012, Spectral Methods: Fundamentals in Single Domains

[2] STABLE AND ACCURATE BOUNDARY TREATMENTS FOR COMPACT, HIGH-ORDER FINITE-DIFFERENCE SCHEMES [J].