Quadrature for meshless methods

Ivo Babuška, Uday Banerjee, John E. Osborn, Qiaoluan Li

Research output: Contribution to journalArticle

43 Scopus citations

Abstract

In this paper we discuss quadrature schemes for meshless methods. We consider the Neumann problem and derive an estimate for the energy norm error between the exact solution, u, and the quadrature approximate solution, uh*, in terms of a parameter, h, associated with the family of approximation spaces, and quantities η, τ, and ̇that measure the errors in the stiffness matrix, in the boundary data, and in the right-hand side vector, respectively, due to the quadrature. The major hypothesis in the estimate is that the quadrature stiffness matrix has zero row sums, a hypothesis that can be easily achieved by a simple correction of the diagonal elements.

Original languageEnglish (US)
Pages (from-to)1434-1470
Number of pages37
JournalInternational Journal for Numerical Methods in Engineering
Volume76
Issue number9
DOIs
StatePublished - Dec 1 2008

Keywords

  • Error estimates
  • Galerkin methods
  • Meshless methods
  • Quadrature
  • Row sum-condition

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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