Aplicação recursiva do método dos elementos de contorno em problemas de Poisson

Abstract

This work presents the Recursive application of the Boundary Element Method (BEM), aiming to increase the precision of the numeric calculation in problems governed by Poisson Equation, using different refined degrees of meshing. Classically, the internal points are calculated by reusing the integral equation, after calculating the boundary points. The same technique is used, but now by means of choosing new boundary points again. As it was successful in problems of Laplace and linear elasticity of Navier, here this procedure is used to obtain better results. The mathematic basis of this technique comes from the Weighted Residual Method (WRM), an important numeric method based on minimizing residue along all the domain of the problem. The Galerkin Tensor is used and applied in one and two dimension problems, with the results being compared to the analytical solution. There is better accuracy in the results of the derivative; a slightly improvement on the accuracy is also achieved in the basic variable