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.