The Laplace equation in 3D domains with cracks: dual singularities with log terms and extraction of corresponding edge flux intensity functions

DOI10.1002/mma.3562zbMath1355.65160OpenAlexW1895181844MaRDI QIDQ3179144

Zohar Yosibash, Samuel Shannon, Victor Péron

Publication date: 20 December 2016

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/hal-01111593/file/QDFM_Integer_21_April_2014_mmaauth.pdf

zbMATH Keywords

numerical examplesfinite elementLaplace equationcracklogarithmic singularities3D singularitiesdual eigenvaluesdual singularitiesedge flux/stress intensity functionsquasi-dual function method

Mathematics Subject Classification ID

Brittle fracture (74R10) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Cites Work

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• Corner asymptotics of the magnetic potential in the eddy-current model
• Decompositions in Edge and Corner Singularities for the Solution of the Dirichlet Problem of the Laplacian in a Polyhedron
• Crack Singularities for General Elliptic Systems
• A Quasi-Dual Function Method for Extracting Edge Stress Intensity Functions
• Asymptotics Without Logarithmic Terms for Crack Problems†

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