Crandall, M. G.; Lions, Pierre-Louis Two approximations of solutions of Hamilton-Jacobi equations. (English) Zbl 0556.65076 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 Cited in 1 ReviewCited in 209 Documents 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 × Cite Format Result Cite Review PDF Full Text: DOI