  In this paper we study the convergence of a finite volume approximation of a
convective diffusive elliptic problem with Neumann boundary conditions and L 1
data. To deal with the non-coercive character of the equation and the low
regularity of the right hand-side we mix the finite volume tools and the
renormalized techniques. To handle the Neumann boundary conditions we choose
solutions having a null median and we prove a convergence result.
