Extracting generalized edge flux intensity functions by the quasidual function method along circular 3-D edges

Samuel Shannon (1) , Zohar Yosibash (1) , Monique Dauge (2) , Martin Costabel (2)

1 Department of Computer Science [Beer-Sheva]
2 IRMAR - Institut de Recherche Mathématique de Rennes

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. 31-52. 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.

Domaines: Analyse numérique [math.NA]

Samuel Shannon, Zohar Yosibash, Monique Dauge, Martin Costabel. Extracting generalized edge flux intensity functions by the quasidual function method along circular 3-D edges. 2012. ⟨hal-00725928v1⟩