A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations. Part I: The steady state case

A new upper bound is provided for the L-infinity-norm of the difference bet ween the viscosity solution of a model steady state Hamilton-Jacobi equatio n, u, and any given approximation, v. This upper bound is independent of th e method used to compute the approximation v; it depends solely on the valu es that the residual takes on a subset of the domain which can be easily co mputed in terms of v. Numerical experiments investigating the sharpness of the a posteriori error estimate are given.