Distribuição da tensão elétrica na estrutura de um capacitor

Abstract

The aim of this work is to validate the finite element method by calculating the electrical voltage distribution in the structure of a capacitor. The mathematical model that allows these calculations is the Poisson’s equation The present work was divided into two main parts, in which the exact solution was found first and then the approximate solution was found. The two solutions were compared and the solutions updated with the appropriate approximations were presented in a graph and it was found that the two main methods used here, the separation of variables method and the finite element method, were used correctly and gave us the correct solution. First, we use the Poisson’s Equation to solve the proposed problem. From the Poisson’s Equation we apply the separation of variables method to obtain the exact solution to the problem. This exact solution is used as a reference. Second, we use the finite element method coded in matlab to get the approximate solution. As the approximate solution is practically equal to the exact one then the finite element method also gave us the correct solution to the problem.