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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.

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