Formulações não-singulares do método dos elementos de contorno aplicadas a problemas bidimensionais de potencial

Abstract

In this work three non-singular formulations applied to two-dimensional potential problems are presented and implemented. In these formulations quadratic, cubic and quartic isoparametric boundary elements were used. The first formulation is based on the standard BEM with the collocation point outside the domain, associated with a sub-element technique. The second one is the self-regularized potential-BIE that remains with a weakly singular integral, that can be evaluated by means of a logarithmic quadrature or a standard gaussian quadrature together with a particular transformation proposed by Telles. The third formulation is the self-regularized flux-BIE which is fully regular but requires the C1, _ continuity of the density functions. This requirement is not satisfied by the isoparametric boundary elements, but it is remedied by adopting the relaxed continuity strategy. Three heat problems and one ground water flow problem have been analyzed and the results were compared with exact solutions or with the results obtained by means of the standard CPV-formulation. The standard formulation with the collocation points outside the domain have presented highly accurate results for all problems analyzed. The same can be seen when using the BEM-potential, that is fully equivalent to the standard CPV-formulation. The flux-BIE required quartic elements to show the same level of accuracy obtained when the BEM-potential with quadratic elements were used. In this way the non-singular BIE formulations used in this work may be considered as robust alternatives to strongly singular BIE formulations for 2-D potential problems.