Extracting Generalized Edge Flux Intensity Functions by the Quasidual Function Method along Circular 3-d Edges

Explicit asymptotic series describing solutions to the Laplace equation in the vicinity of a circular edge in a three-dimensional domain was recently provided in Yosibash et al, Int. Jour. Fracture, 168 (2011), pp. 3152. Utilizing it, we extend the quasidual function method (QDFM) for extracting the generalized edge flux intensity functions (GEFIFs) along circular singular edges in the cases of axisymmetric and non-axisymmetric data. This accurate and efficient method provides a functional approximation of the GEFIFs along the circular edge whose order is adaptively increased so to approximate the exact GEFIFs. It is implemented as a post-solution operation in conjunction with the p -version of the finite element method. The mathematical analysis of the QDFM is provided, followed by numerical investigations, demonstrating the efficiency, robustness and high accuracy of the proposed quasi-dual function method. The mathematical machinery developed in the framework of the Laplace operator is important to realize its possible extension for the elasticity system. CONTENTS