Pointwise convergence rate for nonlinear
نویسنده
چکیده
We introduce a new method to obtain pointwise error estimates for vanishing viscosity and nite diierence approximations of scalar conservation laws with piecewise smooth solutions. This method can deal with nitely 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 nite diierence approximations.
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