Yuri Paes Gomes

Abstract

During the Mechanical Engineering course, mainly in the context of Heat Transfer, it is introduced the Poisson Equation, which is essential to solve steady state problems. However, the lacking of a rigorous mathematical study for discussing the existence of a unique solution and the presentation of a numerical method that is compatible with the industry standard removes an important deep conceptual learning about this very important equation. In this sense, this work aims to study the Poisson Equation from the Variational Analysis perspective to prove that there exists an unique solution to the equation (using the Lax-Milgram Theorem) and to derive a numerical solution (using the Galerkin Method)

Advising

Advisors: Anjos, G. R.; Pereira, A.F.