Meshless methods: An overview and recent developments

T. Belytschko*, Y. Krongauz, D. Organ, M. Fleming, P. Krysl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2808 Scopus citations


Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined. It is shown that the three methods are in most cases identical except for the important fact that partitions of unity enable p-adaptivity to be achieved. Methods for constructing discontinuous approximations and approximations with discontinuous derivatives are also described. Next, several issues in implementation are reviewed: discretization (collocation and Galerkin), quadrature in Galerkin and fast ways of constructing consistent moving least-square approximations. The paper concludes with some sample calculations.

Original languageEnglish (US)
Pages (from-to)3-47
Number of pages45
JournalComputer Methods in Applied Mechanics and Engineering
Issue number1-4
StatePublished - Dec 1 1996

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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