On Convergence and Solvability of an Elliptic Equation by Finite Diference Method

Abstract

In this article we deal with questions of convergence, existence and uniqueness of the numerical solutions for a discretized elliptic problem by using finite diference method. In order to show existence and uniqueness of numerical solutions we will use a suitable variational setup (at discrete level) to guarantee the existence of a numerical solution by means of a finite diference method.