Hypersingular residuals - a new approach for error estimation in the boundary element method

Glaucio H. Paulind, L. J. Gray, Vrej Zarikian

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


This paper presents a new approach for a posteriori 'pointwise' error estimation in the boundary element method. The estimator relies upon evaluation of the rasidual of hypersingular integral equations, and is therefore intrinsic to the boundary integral equation approach. A methodology is developed for approximating the error on the boundary as well as in the interior of the domain. Extensive computational experiments have been performed for the two-dimensional Laplace equation and the numerical results indicate that the error estimates successfully track the form of the exact error curve. Moreover, a reasonable estimate of the magnitude of the actual error is also predicted.

Original languageEnglish (US)
Pages (from-to)2005-2029
Number of pages25
JournalInternational Journal for Numerical Methods in Engineering
Issue number12
StatePublished - 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


  • Boundary element method
  • Error estimates
  • Hypersingular integrals
  • Residual estimates
  • Singular and hypersingular residuals
  • Singular integrals


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