Analysis of the discontinuous Galerkin method for Hamilton-Jacobi equations

Hamilton-Jacobi equations are frequently encountered in applications, e.g., calculus of variations, control theory and differential games. in this pap er a discontinuous Galerkin finite element method for nonlinear Hamilton-Ja cobi equations (first proposed by Hu and Shu (to appear)) is investigated. This method handles the complicated geometry by using arbitrary triangulati on, achieves the high order accuracy in smooth regions and the high resolut ion of the derivatives discontinuities. Theoretical results on accuracy and stability properties of the method are proved for certain cases and relate d numerical examples are presented. (C) 2000 IMACS. Published by Elsevier S cience B.V. Ail rights reserved.