Numerical schemes for Hamilton-Jacobi equations on unstructured meshes

Summary.  In this paper, a numerical scheme is presented by applying the finite element method to the viscosity equations of the Hamilton-Jacobi equations on unstructured meshes. By improving the finite element scheme, another numerical scheme is constructed. Under certain limitations, the numerical solutions of the two schemes converge to the viscosity solutions of the Hamilton-Jacobi equations. The latter numerical scheme has weaker restrictions than the former scheme for convergence. Numerical examples are provided to test the stability, convergence and sensitivity to different meshes. Received November 5, 2001 / Revised version received March 5, 2002 / Published online October 29, 2002 RID="*" ID="*" Current address: Department of Applied Mathematics, University of Petroleum, Dongying 257062, Shandong, P.R.China; e-mail: xianggui_li@sina.com Mathematics Subject Classification (1991): 65M60