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