Effect of numerical integration on meshless methods

Ivo Babuška, Uday Banerjee, John E. Osborn, Qinghui Zhang

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


In this paper, we present the effect of numerical integration on meshless methods with shape functions that reproduce polynomials of degree k ≥ 1. The meshless method was used on a second order Neumann problem and we derived an estimate for the energy norm of the error between the exact solution and the approximate solution from the meshless method under the presence of numerical integration. This estimate was obtained under the assumption that the numerical integration scheme satisfied a form of Green's formula. We also indicated how to obtain numerical integration schemes satisfying this property.

Original languageEnglish (US)
Pages (from-to)2886-2897
Number of pages12
JournalComputer Methods in Applied Mechanics and Engineering
Issue number37-40
StatePublished - Aug 1 2009


  • Error estimates
  • Galerkin methods
  • Meshless methods
  • Numerical integration
  • Quadrature

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


Dive into the research topics of 'Effect of numerical integration on meshless methods'. Together they form a unique fingerprint.

Cite this