The Laplace equation in 3D 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)....

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Veröffentlicht in:	Mathematical methods in the applied sciences 2016-11, Vol.39 (17), p.4951-4963
Hauptverfasser:	Shannon, Samuel, Peron, Victor, Yosibash, Zohar
Format:	Artikel
Sprache:	eng
Schlagworte:	3D singularities Cracks dual eigenvalues dual singularities edge flux/stress intensity functions Eigenvalues Flux Laplace equation logarithmic singularities Mathematical analysis Mathematical models quasi-dual function method Shadows Singularities
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creator	Shannon, Samuel Peron, Victor Yosibash, Zohar
description	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 © 2015 John Wiley & Sons, Ltd.
doi_str_mv	10.1002/mma.3562
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subjects	3D singularities Cracks dual eigenvalues dual singularities edge flux/stress intensity functions Eigenvalues Flux Laplace equation logarithmic singularities Mathematical analysis Mathematical models quasi-dual function method Shadows Singularities
title	The Laplace equation in 3D domains with cracks: dual singularities with log terms and extraction of corresponding edge flux intensity functions
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