The variational approach of an elliptic problem and its solution by finite elements

Abstract: In this paper, we deal with an elliptic problem with the Dirichlet boundary condition. We operate in Sobolev spaces and the main analytic tool we use is the Lax-Milgram lemma. First, we present the variational approach of the problem which allows us to apply different functional analysis techniques. Then we study thoroughly the well-posedness of the problem. We conclude our work with a solution of the problem using numerical analysis techniques and the free software freefem++.