A NEW APPROACH TO NUMERICAL CONSERVATION-LAWS

We construct a general theory of apriori error estimates for scalar co nservation laws by suitably modifying the original Kuznetsov approxima tion theory. As a first application, we show that error estimates for conservation laws can be obtained without having to use explicitly any regularity properties of the approximate solution. The feasibility of the approach is illustrated by considering the Engquist-Osher scheme for which an optimal error estimate is obtained, regardless of the reg ularity properties of the discrete solution.