Abstract
We introduce a new method to obtain pointwise error estimates for vanishing viscosity and finite difference approximations of scalar conservation laws with piecewise smooth solutions. This method can deal with finitely many shocks with possible collisions. The key ingredient in our approach is an interpolation inequality between the L 1 and Lip +-bounds, which enables us to convert a global result into a (non-optimal) local estimate. A bootstrap argument yields optimal pointwise error bound for both the vanishing viscosity and finite difference approximations.KeywordsTravel Wave SolutionEntropy SolutionFinite Difference ApproximationShock CurveSingular SupportThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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