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

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Abstract
A new upper bound is provided for the L-norm of the difference between the viscosity solution of a model 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 that the residual takes on a subset of the domain which can be easily computed in terms of . Numerical experiments investigating the sharpness of the a posteriori error estimate are given.