Superelements for the finite element solution of two-dimensional elliptic problems with boundary singularities

Zohar Yosibash*, Bernard Schiff

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A novel singular superelement (SSE) formulation has been developed to overcome the loss of accuracy encountered when applying the standard finite element schemes to two-dimensional elliptic problems possessing a singularity on the boundary arising from an abrupt change of boundary conditions or a reentrant corner. The SSE consists of an inner region over which the known analytic form of the solution in the vicinity of the singular point is utilized, and a transition region in which blending functions are used to provide a smooth transition to the usual linear or quadratic isoparametric elements used over the remainder of the domain. Solution of the finite element equations yield directly the coefficients of the asymptotic series, known as the flux/stress intensity factors in linear heat transfer or elasticity theories, respectively. Numerical examples using the SSE for the Laplace equation and for computing the stress intensity factors in the linear theory of elasticity are given, demonstrating that accurate results can be attained for a moderate computational effort.

Original languageEnglish
Pages (from-to)315-335
Number of pages21
JournalFinite Elements in Analysis and Design
Volume26
Issue number4
DOIs
StatePublished - 15 Aug 1997
Externally publishedYes

Keywords

  • Elasticity
  • Finite element methods
  • Laplace equation
  • Singularities
  • Stress intensity factors

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