【Abstract】 In this paper, non-oscillatory numerical schemes with high order of accuracy are presented for solving Hamilton-Jacobi equations on structured meshes; An adaptive local refinement method is developed for local regions where solutions of Hamilton-Jacobi equations varies sharply. Numerical results illustrate that the non-oscillatory schemes are stable and the adaptive local refinement method im- proves the accuracy of numerical solutions and the resolution for discontinuity.更多还原