Vertex Singularities for the 3-D Laplace Equation

Zohar Yosibash

doi:https://doi.org/10.1007/978-1-4614-1508-4_12

Vertex Singularities for the 3-D Laplace Equation

Zohar Yosibash

Department of Mechanical Engineering

Ben-Gurion University of the Negev

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Although singular points in 2-D domains have been extensively investigated, the vertex singularities in 3-D domains have received scant attention due to their complexity. To the best of our knowledge, numerical methods for the investigation of vertices of conical notches, specifically the exponents of the singularity, were first introduced in [23]. Stephan and Whiteman [170] and Beagles and Whiteman [25] investigated analytically several vertices for the Laplace equation in 3-D, mainly with homogeneous Dirichlet boundary conditions, and analyzed a finite element method for the computation of eigenvalues by discretizing the Laplace-Beltrami equation (error estimates provided but no numerical results).

Original language	American English
Title of host publication	Interdisciplinary Applied Mathematics
Publisher	Springer Nature
Pages	291-314
Number of pages	24
DOIs	https://doi.org/10.1007/978-1-4614-1508-4_12
State	Published - 1 Jan 2012

Publication series

Name	Interdisciplinary Applied Mathematics
Volume	37

Keywords

Associate Legendre Function
Crack Front
Elasticity System
Laplace Equation
Legendre Function

All Science Journal Classification (ASJC) codes

Applied Mathematics
Computational Mathematics
Computational Theory and Mathematics
Management Science and Operations Research

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https://doi.org/10.1007/978-1-4614-1508-4_12

Cite this

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title = "Vertex Singularities for the 3-D Laplace Equation",

abstract = "Although singular points in 2-D domains have been extensively investigated, the vertex singularities in 3-D domains have received scant attention due to their complexity. To the best of our knowledge, numerical methods for the investigation of vertices of conical notches, specifically the exponents of the singularity, were first introduced in [23]. Stephan and Whiteman [170] and Beagles and Whiteman [25] investigated analytically several vertices for the Laplace equation in 3-D, mainly with homogeneous Dirichlet boundary conditions, and analyzed a finite element method for the computation of eigenvalues by discretizing the Laplace-Beltrami equation (error estimates provided but no numerical results).",

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AB - Although singular points in 2-D domains have been extensively investigated, the vertex singularities in 3-D domains have received scant attention due to their complexity. To the best of our knowledge, numerical methods for the investigation of vertices of conical notches, specifically the exponents of the singularity, were first introduced in [23]. Stephan and Whiteman [170] and Beagles and Whiteman [25] investigated analytically several vertices for the Laplace equation in 3-D, mainly with homogeneous Dirichlet boundary conditions, and analyzed a finite element method for the computation of eigenvalues by discretizing the Laplace-Beltrami equation (error estimates provided but no numerical results).

KW - Associate Legendre Function

KW - Crack Front

KW - Elasticity System

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KW - Legendre Function

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M3 - Chapter

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BT - Interdisciplinary Applied Mathematics

PB - Springer Nature

ER -

Vertex Singularities for the 3-D Laplace Equation

Abstract

Publication series

Keywords

All Science Journal Classification (ASJC) codes

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