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Recently, Cockburn, Coquel and LeFloch proved convergence and error estimates for higher-order nite volume schemes. Their result is based on entropy inequalities which are derived under restrictive assumptions on ei- ther the flux function or the numerical fluxes. Moreover, they assume that the spatial grid satises a standard regularity assumption. Using instead en- tropy inequalities derived in previous work by Kroner, Noelle and Rokyta and a weaker condition on the grid, we can generalize and simplify the error esti- mates.

A note on entropy inequalities and error estimates for higher-order accurate finite volume schemes on irregular families of grids