CONVERGENCE OF AN ENGQUIST-OSHER SCHEME FOR A MULTI-DIMENSIONAL TRIANGULAR SYSTEM OF CONSERVATION LAWS

被引：11

作者：

Coclite, G. M. ^{[1
]}

Mishra, S. ^{[2
]}

Risebro, N. H. ^{[2
]}

机构：

[1] Univ Bari, Dept Math, I-70125 Bari, Italy

[2] Univ Oslo, Ctr Math Applicat, N-0316 Oslo, Norway

来源：

MATHEMATICS OF COMPUTATION | 2010年 / 79卷 / 269期

关键词：

DIFFERENCE SCHEME; DISCONTINUOUS FLUX;

D O I：

10.1090/S0025-5718-09-02251-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a multi-dimensional triangular system of conservation laws. This system arises as a model of three-phase flow in porous media and includes multi-dimensional conservation laws with discontinuous coefficients as a special case. The system is neither strictly hyperbolic nor symmetric. We propose an Engquist-Osher type scheme for this system and show that the approximate solutions generated by the scheme converge to a weak solution. Numerical examples are also presented.

引用

页码：71 / 94

页数：24

共 21 条

[1] Adimurthi, 2005, J HYPERBOL DIFFER EQ, V2, P783
[2] [Anonymous], 2002, Applied Mathematical Sciences
[3] Benzoni-Gavage S., 2007, Multidimensional Hyperbolic Partial Differential Equations. First-Order Systems and Applications Oxford Mathematical Monographs
[4] Well-posedness in BVt and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units
Bürger, R
Karlsen, KH
Risebro, NH
Towers, JD
[J]. NUMERISCHE MATHEMATIK, 2004, 97 (01) : 25 - 65
[5] Chen Z., 2006, COMPUTATIONAL SCI EN
[6] COCLITE GM, UNIONE MAT IN PRESS
[7] SOME RELATIONS BETWEEN NONEXPANSIVE AND ORDER PRESERVING MAPPINGS
CRANDALL, MG
TARTAR, L
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1980, 78 (03) : 385 - 390
[8] Diehl S, 1995, SIAM J APPL MATH, V56, P1980
[9] Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes
Eymard, R
Gallouet, T
Ghilani, M
Herbin, R
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 1998, 18 (04) : 563 - 594
[10] SOLUTION OF THE CAUCHY-PROBLEM FOR A CONSERVATION LAW WITH A DISCONTINUOUS FLUX FUNCTION
GIMSE, T
RISEBRO, NH
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1992, 23 (03) : 635 - 648

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