Analysis of the discontinuous Galerkin method for Hamilton–Jacobi equations Original Research Article

Hamilton–Jacobi equations are frequently encountered in applications, e.g., calculus of variations, control theory and differential games. In this paper a discontinuous Galerkin finite element method for nonlinear Hamilton–Jacobi equations (first proposed by Hu and Shu (to appear)) is investigated. This method handles the complicated geometry by using arbitrary triangulation, achieves the high order accuracy in smooth regions and the high resolution of the derivatives discontinuities. Theoretical results on accuracy and stability properties of the method are proved for certain cases and related numerical examples are presented.