The Laplace equation in 3 - D domains with cracks : Dual singularities with log terms and extraction of corresponding edge flux intensity functions

The singular solution of the Laplace equation with a straight-crack is represented by a series of eigenpairs, shadows and their associated edge flux intensity functions (EFIFs). We address the computation of the EFIFs associated with the integer eigenvalues by the quasi-dual function method (QDFM).The QDFM is based on the dual eigenpairs and shadows, and we exhibit the presence of logarithmic terms in the dual singularities associated with the integer eigenvalues. These are then used with the QDFM to extract EFIFs from p-version finite element solutions. Numerical examples are provided. Copyright c ⃝ 0000 John Wiley & Sons, Ltd.