Complete analytic integrations for the 2D BEM representation of the Laplace equation with linear shape functions

Abstract This paper proposes a complete set of analytical formulae to handle the 2D BEM representation of the Laplace when geometry is approximated by linear elements and unknown function by continuous linear shape functions. Results already published in literature are corrected and the expressions for collinear domain integrations are introduced. The numerical validation is performed on a problem with analytic solution.