Computing flux intensity factors by a boundary method for elliptic equations with singularities

M. Arad*, Z. Yosibash, G. Ben-Dor, A. Yakhot

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A simple method for computing the flux intensity factors associated with the asymptotic solution of elliptic equations having a large convergence radius in the vicinity of singular points is presented. The Poisson and Laplace equations over domains containing boundary singularities due to abrupt change of the boundary geometry or boundary conditions are considered. The method is based on approximating the solution by the leading terms of the local symptotic expansion, weakly enforcing boundary conditions by minimization of a norm on the domain boundary in a least-squares sense. The method is applied to the Motz problem, resulting in extremely accurate estimates for the flux intensity factors. It is shown that the method converges exponentially with the number of singular functions and requires a low computational cost. Numerical results to a number of problems concerned with the Poisson equation over an L-shaped domain, and over domains containing multiple singular points, demonstrate accurate estimates for the flux intensity factors. €> 1998 John Wiley & Sons, Ltd.

Original languageEnglish
Pages (from-to)657-670
Number of pages14
JournalCommunications in Numerical Methods in Engineering
Volume14
Issue number7
DOIs
StatePublished - Jul 1998
Externally publishedYes

Keywords

  • Eliptic PDEs
  • Flux intensity factors
  • Multiple singular points
  • Singularities

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