  We deal with the problem of approximating a scalar conservation law by a
conservation law with nonlocal flux. As convolution kernel in the nonlocal
flux, we consider an exponential-type approximation of the Dirac distribution.
This enables us to obtain a total variation bound on the nonlocal term. By
using this, we prove that the (unique) weak solution of the nonlocal problem
converges strongly in $C(L^{1}_{\text{loc}})$ to the entropy solution of the
local conservation law. We conclude with several numerical illustrations which
underline the main results and, in particular, the difference between the
solution and the nonlocal term.
