  A numerical analysis of upwind type schemes for the nonlinear nonlocal
aggregation equation is provided. In this approach, the aggregation equation is
interpreted as a conservative transport equation driven by a nonlocal nonlinear
velocity field with low regularity. In particular, we allow the interacting
potential to be pointy, in which case the velocity field may have
discontinuities. Based on recent results of existence and uniqueness of a
Filippov flow for this type of equations, we study an upwind finite volume
numerical scheme and we prove that it is convergent at order 1/2 in Wasserstein
distance. This result is illustrated by numerical simulations, which show the
optimality of the order of convergence.
