Anti-diffusive High Order WENO Schemes for Hamilton-Jacobi Equations

Abstract

In this paper, we generalize the technique of anti-diffusive flux corrections for high order finite difference WENO schemes solving conservation laws in [21], 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.