Abstract
The feasibility of using combinations of the boundary integral equation (BIE) and the normal derivative of the boundary integral equation (DBIE) is investigated for the two-dimensional Laplace equation. By using the combinations of these two equations it is possible to derive Fredholm integral equations of either the first or second kind regardless of the boundary conditions. Although the Fredholm equations of the second kind are well conditioned, in general they provide less accurate interior results than the Fredholm equations of the first kind and the classical direct boundary element method (DBEM). On the other hand, the Fredholm equations of the first kind can provide poor solutions in regions close to the boundary where large gradients exist in the boundary flux.
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