Convex ENO Schemes for Hamilton-Jacobi Equations

In one dimension, viscosity solutions of Hamilton-Jacobi (HJ) equations can be thought as primitives of entropy solutions for conservation laws. Based on this idea, both theoretical and numerical concepts used for conservation laws can be passed to HJ equations even in multi dimensions. In this paper, we construct convex ENO (CENO) schemes for HJ equations. This construction is a generalization from the work by Xu-Dong Liu and S. Osher on CENO schemes for conservation laws. Several numerical experiments are performed. L1 and L∞ error and convergence rate are calculated as well. Keywords. convex ENO schemes, Hamilton-Jacobi equations, conservation laws, two-dimensional Riemann problems

• Type: Journal
• Year: 2007
• Where: JSCIC
• Authors: Chi-Tien Lin, Xu-Dong Liu
• Keywords: Conservation Laws, Equations, HJ Equations, JSCIC 2007