NUMERICAL PASSAGE FROM SYSTEMS OF CONSERVATION-LAWS TO HAMILTON-JACOBI EQUATIONS, AND RELAXATION SCHEMES

Authors
JIN S XIN ZP
Citation
S. Jin et Zp. Xin, NUMERICAL PASSAGE FROM SYSTEMS OF CONSERVATION-LAWS TO HAMILTON-JACOBI EQUATIONS, AND RELAXATION SCHEMES, SIAM journal on numerical analysis (Print), 35(6), 1998, pp. 2385-2404
Citations number
32
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM journal on numerical analysis (Print) → ACNP
ISSN journal
00361429
Volume
35
Issue
6
Year of publication
1998
Pages
2385 - 2404
Database
ISI
SICI code
0036-1429(1998)35:6<2385:NPFSOC>2.0.ZU;2-Z
Abstract
In this paper we study the numerical transition from a Hamilton-Jacobi (H-J) equation to its associated system of conservation laws in arbit rary space dimensions. We first study how, in a very generic setting, one can recover the viscosity solutions of the H-J equation using the numerical solutions to the system of conservation laws. We then introd uce a simple, second-order relaxation scheme to solve the underlying w eakly hyperbolic system of conservation laws.