AN ERROR ESTIMATE FOR FINITE-VOLUME METHODS FOR MULTIDIMENSIONAL CONSERVATION-LAWS

被引：3

作者：

COCKBURN, B

COQUEL, F

LEFLOCH, P

机构：

[1] OFF NATL ETUD & RECH AEROSP,F-92322 CHATILLON,FRANCE

[2] NYU,COURANT INST MATH SCI,NEW YORK,NY 10012

来源：

MATHEMATICS OF COMPUTATION | 1994年 / 63卷 / 207期

关键词：

MULTIDIMENSIONAL CONSERVATION LAW; DISCONTINUOUS SOLUTION; FINITE VOLUME METHOD; ERROR ESTIMATE;

D O I：

10.2307/2153563

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, an L(infinity)(L1)-error estimate for a class of finite volume methods for the approximation of scalar multidimensional conservation laws is obtained. These methods can be formally high-order accurate and are defined on general triangulations. The error is proven to be of order h1/4, where h represents the ''size''of the mesh, via an extension of Kuznetsov approximation theory for which no estimate of the total variation and of the modulus of continuity in time are needed. The result is new even for the finite volume method constructed from monotone numerical flux functions.

引用

页码：77 / 103

页数：27

共 50 条

[1]

CHEN GQ, 1993, MATH COMPUT, V61, P629, DOI 10.1090/S0025-5718-1993-1185240-3

[2]

CHEN GQ, UNPUB ENTROPY FLUX 2

[3]

CHEN GQ, UNPUB COMM PURE APPL

[4] STABILITY THEOREM AND TRUNCATION ERROR ANALYSIS FOR THE GLIMM SCHEME AND FOR A FRONT TRACKING METHOD FOR FLOWS WITH STRONG DISCONTINUITIES [J].