A discontinuous Galerkin finite element method for Hamilton-Jacobi equations

In this paper, we present a discontinuous Galerkin finite element method fo r solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving co nservation laws. The method has the flexibility of treating complicated geo metry by using arbitrary triangulation, can achieve high-order accuracy wit h a local, compact stencil, and is suited for efficient parallel implementa tion. One- and two-dimensional numerical examples are given to illustrate t he capability of the method. At least kth order of accuracy is observed for smooth problems when kth degree polynomials are used, and derivative singu larities are resolved well without oscillations, even without limiters.