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Recently, Cockburn, Coquel and LeFloch proved convergence and error estimates for higher-order finite volume schemes. Their result is based on entropy inequalities which are derived under restrictive assumptions on either the flux function or the numerical fluxes. Moreover, they assume that the spatial grid satisfies a standard regularity assumption. Using instead entropy inequalities derived in previous work by Kröner, Noelle and Rokyta and a weaker condition on the grid, we can generalize anddoi:10.1090/s0025-5718-96-00737-5 fatcat:kdtqr4o6p5hg7icanoifzbq5yy