A local discontinuous Galerkin method for directly solving Hamilton-Jacobi equations

In this paper we propose a new local discontinuous Galerkin method to directly solve Ham-ilton–Jacobi equations. The scheme is a natural extension of the monotone scheme. For the linear case with constant coefficients, the method is equivalent to the discontinuous Galer-kin method for conservation laws. Thus, stability and error analysis are obtained under the framework of conservation laws. For both convex and noneconvex Hamiltonian, optimal (k + 1)th order of accuracy for smooth solutions are obtained with piecewise kth order polynomial approximations. The scheme is numerically tested on a variety of one and two dimensional problems. The method works well to capture sharp corners (discontinu-ous derivatives) and have the solution converges to the viscosity solution.