Two approximations of solutions of Hamilton-Jacobi equations. (English) Zbl 0556.65076

Crandall, M. G.; Lions, Pierre-Louis

Math. Comput. 43, 1-19 (1984).

The paper is concerned with the approximation of solutions of the Cauchy problem for first order partial differential equations of Hamilton-Jacobi type. Two sorts of approximations are considered - finite difference schemes and the method of vanishing viscosity. The paper establishes the convergence of these difference approximations to suitable generalized solutions by obtaining explicit error estimates.

Reviewer: A.Varga

MSC:

65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
35L45	Initial value problems for first-order hyperbolic systems
70H20	Hamilton-Jacobi equations in mechanics

Keywords:

convergence; error estimates; method of vanishing viscosity