Finite volume scheme and renormalized solutions for nonlinear elliptic Neumann problem with L1 data

TL;DR

This paper develops a finite volume scheme combined with renormalized techniques to prove convergence for a nonlinear elliptic Neumann problem with low regularity L1 data, addressing non-coercivity and boundary conditions.

Contribution

It introduces a novel approach integrating finite volume methods with renormalized solutions for low-regularity elliptic problems with Neumann boundary conditions.

Findings

Proves convergence of the finite volume scheme for the problem.

Handles non-coercive equations with L1 data.

Establishes solutions with null median for Neumann conditions.

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.