Finite volume scheme and renormalized solutions for nonlinear elliptic Neumann problem with $$L^1$$ data

Abstract

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. We present also some numerical experiments in dimension 2 to illustrate the rate of convergence.