Analytical integration of elliptic 2D fundamental solution and its derivatives for straight-line elements with constant interpolation
The authors describe the analytical integration of the elliptic 2D fundamental solution and its 1st, 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 the position of the source 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. A comparison of the analytical and the numerical integrations is made.
scientific article; zbMATH DE number 1389988