Extension of the variational self-regular approach for the flux boundary element method formulation

This work deals with a numerical solution technique for the self-regular gradient form of Green's identity, the flux boundary integral equation (flux-BIE). The required Cl P inter-element continuity conditions for the potential derivatives are imposed in the boundary element method (BEM) code through a non-symmetric variational formulation. In spite of using Lagrangian C-0 elements, accurate numerical results were obtained when applied to heat transfer problems with singular or quasi-singular conditions, like boundary points and interior points which may be arbitrarily close to the boundary. The numerical examples proposed show that the developed algorithm based on the self-regular flux-BEE are highly efficient, and quite straightforward in that no integral transformations are necessary to compute the singular integrals and even a small number of integration Gauss points gives very accurate results. The variational self-regular flux-BEE formulation has improved the results for quadratic elements, while only minor improvements were obtained for higher order elements. The proposed approach is also compared with other formulations showing to be a robust alternative as a BEM approach in heat transfer problems.