Analytical integration of elliptic 2D fundamental solution and its derivatives for straight-line elements with constant interpolation

This article describes the analytical integration of the elliptic 2D fundamental solution and its Ist, 2nd and 3rd derivatives with the constant function interpolation for straight-line boundary elements. As a result of the character of the integrated function, the integrals are characterized with regard to position of the sourer point. If it lies on the boundary Gamma, then the integrals are: weak-(log r), strong-(1/r) and hyper-(1/r(2)) singular. Otherwise, the integrals are regular. The 3rd derivatives of the fundamental solution are needed for the calculation of partial derivative(2)ul/partial derivative x(2) and partial derivative(2)ul/partial derivative y(2) of harmonic function u in the domain Omega. A comparison of the analytical and the numerical integrations is made. (C) 1999 Elsevier Science Ltd. All rights reserved.