|
Abstract : |
Abstract. In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. At least k-th order of accuracy is observed for smooth problems when k-th degree polynomials are used, and derivative singularities are resolved well without oscillations even without limiters. Key words. Hamilton-Jacobi Equations, discontinuous Galerkin, high order accuracy., |
