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We deal with the numerical investigation of the local limit of nonlocalconservation laws. Previous numerical experiments suggest convergence in thelocal limit. However, recent analytic results state that (i) in generalconvergence does not hold because one can exhibit counterexamples; (ii)convergence can be recovered provided viscosity is added to both the local andthe nonlocal equations. Motivated by these analytic results, we investigate therole of numerical viscosity in the numerical study of the local limit ofnonlocal conservation laws. In particular, we show that the numerical viscosityof Lax-Friedrichs type schemes jeopardizes the reliability of the numericalscheme and erroneously detects convergence in cases where convergence is ruledout by analytic results. We also test Godunov type schemes, less affected bynumerical viscosity, and show that in some cases they provide more reliableresults.

On the role of numerical viscosity in the study of the local limit of nonlocal conservation laws