A quasi-dual function method for extracting edge stress intensity functions

Martin Costabel*, Monique Dauge, Zohar Yosibash

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We present a method for the computation of the coefficients of singularities along the edges of a polyhedron for second-order elliptic boundary value problems. The class of problems considered includes problems of stress concentration along edges or crack fronts in general linear three-dimensional elasticity. Our method uses an incomplete construction of three-dimensional dual singular functions, based on explicitly known dual singular functions of two-dimensional problems tensorized by test functions along the edge and combined with complementary terms improving their orthogonality properties with respect to the edge singularities. Our method is aimed at the numerical computation of the stress intensity functions. It is suitable for a postprocessing procedure in the finite element approximation of the solution of the boundary value problem.

Original languageEnglish
Pages (from-to)1177-1202
Number of pages26
JournalSIAM Journal on Mathematical Analysis
Issue number5
StatePublished - 2004
Externally publishedYes


  • Dual singularities
  • Edge singularities
  • Stress intensity factors


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