The Laplace equation in 3-D domains with cracks: Dual shadows with log terms and extraction of corresponding edge flux intensity functionsReport as inadecuate




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1 Department of Mechanical Engineering, Ben-Gurion University of the Negev 2 LMAP - Laboratoire de Mathématiques et de leurs Applications Pau 3 Magique 3D - Advanced 3D Numerical Modeling in Geophysics LMAP - Laboratoire de Mathématiques et de leurs Applications Pau, Inria Bordeaux - Sud-Ouest

Abstract : 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 show that the dual shadows associated with the integer eigenvalues contain logarithmic terms. These are then used with the QDFM to extract EFIFs from p-version finite element solutions. Numerical examples are provided. Dedicated to the 65th birthday of prof. Martin Costabel.

Keywords : dual eigenvalues quasi-dual function method edge flux-stress intensity functions Logarithmic singularities 3-D singularities





Author: Samuel Shannon - Victor Péron - Zohar Yosibash -

Source: https://hal.archives-ouvertes.fr/



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