Numerical analysis of a nonlinear discrete duality finite volume scheme for Leray-Lions type elliptic problems in Orlicz spaces

Abstract

In this work, we develop a finite volume approximation for general nonlinear Leray-Lions problems in the Orlicz-Sobolev framework. We prove the existence and uniqueness and some a priori estimate of the approximate solution. We establish a discrete version of Poincaré inequality and a result of discrete compactness which allows us to prove the convergence towards the weak solution of the continuous problem. Some numerical tests are provided on general meshes.