Adaptivity for structured meshfree particle methods in 2D and 3D

T. Rabczuk, Ted Belytschko

Research output: Contribution to journalArticlepeer-review

240 Citations (Scopus)


The implementation of h-adaptivity for meshfree particle methods within a structured framework is described. In this framework, the initial particle arrangement is structured along with a background mesh, and outside boundaries and interior interfaces are described by implicit functions. The advantage of meshfree approximations in this framework lies in the ease of implementing h-adaptivity and the simplicity of the data structures. Particles can easily be added and removed without complications in the data structure, although there are some issues in the quadrature. An a posteriori error estimation is used for the adaptive refinement. An adaptive refinement strategy is applied to several linear elastic problems with high stress and strain gradients and singularities. Several non-linear examples are also given.

Original languageEnglish
Pages (from-to)1559-1582
Number of pages24
JournalInternational Journal for Numerical Methods in Engineering
Issue number11
Publication statusPublished - 2005 Jul 21


  • Adaptivity
  • EFG
  • Error estimation
  • Level sets
  • Meshfree particle methods

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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