A note on the variational formulation of PDEs and solution by finite elements

Abstract

Mathematical modeling of differential equations is, in some cases, complex to develop through an analytical solution. In this article a description of the variational method is presented, which is used for the qualitative study of partial differential equations: existence, uniqueness and regularity of the solution [1]. The analysis of linear second-order elliptic partial differential equations is shown as an illustration. Finally, an application of the weak formulation of the Poisson equation is shown by the finite element method.