Numerical Passage from Systems of Conservation Laws to Hamilton--Jacobi Equations, and Relaxation Schemes

Authors:
Shi Jin;Zhouping Xin
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
1998

Citing 0
Cited 18

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Hermite WENO schemes for Hamilton-Jacobi equations on unstructured meshes

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Abstract

In this paper we study the numerical transition from a Hamilton--Jacobi (H--J) equation to its associated system of conservation laws in arbitrary 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 introduce a simple, second-order relaxation scheme to solve the underlying weakly hyperbolic system of conservation laws.