  In this article we consider the initial value problem for a scalar
conservation law in one space dimension with a spatially discontinuous flux.
There may be infinitely many flux discontinuities, and the set of
discontinuities may have accumulation points. Thus the existence of traces
cannot be assumed. In [6] Audusse and Perthame proved a uniqueness result that
does not require the existence of traces, using adapted entropies. We
generalize the Godunov-type scheme of Adimurthi, Jaffre and Gowda [2] for this
problem with the following assumptions on the flux function, (i) the flux is BV
in the spatial variable and (ii) the critical point of the flux is BV as a
function of the space variable. We prove that the Godunov approximations
converge to an adapted entropy solution, thus providing an existence result,
and extending the convergence result of Adimurthi, Jaffre and Gowda.
