  This paper is concerned with a strongly degenerate convection-diffusion
equation in one space dimension whose convective flux involves a non-linear
function of the total mass to one side of the given position. This equation can
be understood as a model of aggregation of the individuals of a population with
the solution representing their local density. The aggregation mechanism is
balanced by a degenerate diffusion term accounting for dispersal. In the
strongly degenerate case, solutions of the non-local problem are usually
discontinuous and need to be defined as weak solutions satisfying an entropy
condition. A finite difference scheme for the non-local problem is formulated
and its convergence to the unique entropy solution is proved. The scheme
emerges from taking divided differences of a monotone scheme for the local PDE
for the primitive. Numerical examples illustrate the behaviour of entropy
solutions of the non-local problem, in particular the aggregation phenomenon.
