Numerical passage from systems of conservation laws to Hamilton-Jacobi equations, and relaxation schemes

摘要

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. [References: 32]