A Weighted Essentially Nonoscillatory, Large Time-Step Scheme for Hamilton-Jacobi Equations

We investigate the application of weighted essentially nonoscillatory (WENO) reconstructions to a class of semi-Lagrangian schemes for first order time-dependent Hamilton–Jacobi equations. In particular, we derive a general form of the scheme, study sufficient conditions for its convergence with high-order reconstructions, and perform numerical tests to study its efficiency. In addition, we prove that the weights of the WENO interpolants are positive for any order. 1. Introduction. In this paper we treat a class of high-order, large time-step Godunov schemes for time-dependent Hamilton–Jacobi equation of first order. Although several extensions are possible, we will focus on the model problem v t + H(∇v) = 0 in R