Open Access
June2005 Anti-diffusive High Order WENO Schemes for Hamilton-Jacobi Equations
Zhengfu Xu, Chi-Wang Shu
Methods Appl. Anal. 12(2): 169-190 (June2005).


In this paper, we generalize the technique of anti-diffusive flux corrections for high order finite difference WENO schemes solving conservation laws in, to solve Hamilton-Jacobi equations. The objective is to obtain sharp resolution for kinks, which are derivative discontinuities in the viscosity solutions of Hamilton-Jacobi equations. We would like to resolve kinks better while maintaining high order accuracy in smooth regions. Numerical examples for one and two space dimensional problems demonstrate the good quality of these Hamiltonian corrected WENO schemes.


Download Citation

Zhengfu Xu. Chi-Wang Shu. "Anti-diffusive High Order WENO Schemes for Hamilton-Jacobi Equations." Methods Appl. Anal. 12 (2) 169 - 190, June2005.


Published: June2005
First available in Project Euclid: 5 April 2007

zbMATH: 1119.65378
MathSciNet: MR2257526

Primary: 65M06

Keywords: anti-diffusive flux correction , finite difference , Hamiltonian correction , Hamilton-Jacobi equations , high order accuracy , kinks , WENO scheme

Rights: Copyright © 2005 International Press of Boston

Vol.12 • No. 2 • June2005
Back to Top