Primal and Shadow functions, Dual and Dual-Shadow functions for a circular crack and a circular 90^o V-notch with Neumann boundary conditions

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

This report presents explicit analytical expressions for the primal, primal shadows, dual and dual shadows functions for the Laplace equation in the vicinity of a circular singular edge with Neumann boundary conditions on the faces that intersect at the singular edge. Two configurations are investigated: a penny-shaped crack and a 90^o V-notch.

Mots clés: Penny-shaped crack; V-notch; Edge singularities; Shadow functions

Domaines: Analyse numérique [math.NA]

Samuel Shannon, Zohar Yosibash, Monique Dauge, Martin Costabel. Primal and Shadow functions, Dual and Dual-Shadow functions for a circular crack and a circular 90^o V-notch with Neumann boundary conditions. 2012. ⟨hal-00765619v2⟩