Convergence of the discrete finite volume solution to the renormalized solution for a noncoercive elliptic problem with Neumann boundary conditions and L1-data

Abstract

We are interested in this paper to show that the approximate solution, by the finite volumes method, converges to the renormalized solution of convective-diffusive elliptic problem with Neumann boundary conditions and L¹-data. In the first part, we recall formulas and give some notations which are useful for the next of the work. We also, give some definitions and properties on Partial Differentials Equations. In the second part we show the bases principle of the main methods of discretization, more precisely, the finite volume method. In the third part, we study a noncoercive elliptic convection-diffusion equation with Neumann boundary conditions and L¹-data. By adapting the strategy developed in the finite volume method, we show that the approximate solution converges to the unique renormalized solution.