Journal ArticleDOI
An efficient method for subtracting off singularities at corners for Laplace's equation
TLDR
In this article, a methode based on un algorithme permettant de calculer les coefficients du developpement asymptotique de la solution a la singularite is proposed.About:
This article is published in Journal of Computational Physics.The article was published on 1988-10-01. It has received 37 citations till now. The article focuses on the topics: Laplace's equation & Partial differential equation.read more
Citations
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Trefftz and Collocation Methods
TL;DR: In this article, the authors present a comprehensive review of boundary integral equation and boundary element methods and compare them with other kinds of boundary methods, including CTM, CM, and CTM coupling techniques.
Journal ArticleDOI
Singularities and treatments of elliptic boundary value problems
TL;DR: In this article, a survey of treatments for singularity problems of elliptic equations of polygons is provided, where the authors take the Laplace equation on polygons as an example, and choose Motz's problem as a benchmark of singularity problem.
Journal ArticleDOI
An efficient finite element method for treating singularities in Laplace's equation
TL;DR: In this article, a new finite element method for solving partial differential equations with singularities caused by abrupt changes in boundary conditions or sudden change in boundary shape is presented, which eliminates the need for high-order integration, improves the overall accuracy, and yields very accurate estimates for the singular coefftcients.
Journal ArticleDOI
The solution of Laplacian problems over L-shaped domains with a singular function boundary integral method
TL;DR: In this article, the singular function boundary integral method is applied for the solution of a Laplace equation problem over an L-shaped domain, where the solution is approximated by the leading terms of the local asymptotic solution expansion, while the Dirichlet boundary conditions are enforced by means of Lagrange multipliers.
Journal ArticleDOI
Three-dimensional singular boundary elements for corner and edge singularities in potential problems
E.T. Ong,Kian Meng Lim +1 more
TL;DR: In this paper, the authors describe the formulation and implementation of new singular elements for three-dimensional boundary element analysis of corner and edge singularities in potential problems, where the singular element shape functions incorporate the correct singular behavior at the edges and corners, specifically the eigenvalues, in the formulation.
References
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Journal ArticleDOI
Crack tip finite elements are unnecessary
R. D. Henshell,K. G. Shaw +1 more
TL;DR: In this paper, it was shown that a singularity occurs in isoparametric finite elements if the mid-side nodes are moved sufficiently from their normal position to obtain a more accurate solution to the problem of determining the stress intensity at the tip of a crack.
Journal ArticleDOI
On the use of singular functions with finite element approximations
G.J Fix,S Gulati,G.I Wakoff +2 more
TL;DR: In this paper, a scheme for efficiently modeling singularities in conjunction with finite element approximations to elliptic problems is presented, and three sample physical problems are chosen to illustrate the techniques.
Journal ArticleDOI
The use of infinite grid refinements at singularities in the solution of Laplace's equation
TL;DR: In this article, the use of infinite refinements in the grid of triangles in the neighbourhood of boundary singularities is analyzed and a particular type of infinite grid refinement is proposed and some examples are given.
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The treatment of singularities in the calculation of stress intensity factors using the boundary integral equation method
TL;DR: A version of the boundary integral equation method applicable to elliptic boundary value problems for domains with curved boundaries and mixed boundary conditions (Dirichlet, Neumann and third type) is described in this paper.
Journal ArticleDOI
Treatment of harmonic mixed boundary problems by conformal transformation methods
TL;DR: In this article, a method consisting of three conformal transformations is used for the numerical solution of a class of harmonic mixed boundary value problems containing boundary singularities, although less flexible than the well-known finite-difference and finite element techniques.