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

Abstract

A new upper bound is provided for the L$^\infty$-norm of the difference between the viscosity solution of a model steady state Hamilton-Jacobi equation, $u$, and any given approximation, $v$. This upper bound is independent of the method used to compute the approximation $v$; it depends solely on the values that the residual takes on a subset of the domain which can be easily computed in terms of $v$. Numerical experiments investigating the sharpness of the a posteriori error estimate are given.