A Discontinuous Galerkin Moving Mesh Method for Hamilton-Jacobi Equations

where x = (x1, . . . , xd) ∈ IR , t > 0. HJ equations arise in many practical areas such as differential games, mathematical finance, image enhancement and front propagation. It is well known that solutions of (1) are Lipschitz continuous but derivatives can become discontinuous even if the initial data is smooth. There is a close relation between HJ equations and hyperbolic conservation laws. With this in mind, it not surprising to find that many of the numerical methods used to solve HJ equations are motivated by conservative finite difference or finite volume methods for conservation laws. An increasingly popular approach to solve hyperbolic conservation laws is the discontinuous Galerkin (DG) finite element method. Recently, Hu and Shu [1] proposed a DG method to solve HJ equations by first rewriting (1) as a system of conservation laws