A priori error estimates for approximate solutions to convex conservation laws

We introduce a new technique for proving a priori error estimates between the entropy weak solution of a scalar conservation law and a finite–difference approximation calculated with the scheme of EngquistOsher, Lax-Friedrichs, or Godunov. This technique is a discrete counterpart of the duality technique introducedbyTadmor [SIAMJ.Numer.Anal. 1991]. The error is related to the consistency error of cell averages of the entropy weak solution. This consistency error can be estimated by exploiting a regularity structure of the entropy weak solution. One ends up with optimal error estimates.