The well-posedness of an elliptic problem and its solution using the finite element method

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++.