A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations. I: The steady state case (Q2759084)

A new upper bound is provided for a suitable norm of the difference between the viscosity solution of a steady state Hamilton-Jacobi equation, and any given approximation. This upper bound is independent of the method used to compute the approximation; it depends solely on the values which the residual takes on a subset of the domain which can be easily computed in terms of approximation. Numerical experiments investigating the sharpness of the a posteriori error estimate are carried out. They confirm, even for nonlinear Hamiltonians, that a posteriori error estimates produce effectivity indices which remain reasonably constant as the discretization parameters differ in several order of magnitude.