H-p Clouds - An h-p Meshless Method

C. Armando Duarte, J. Tinsley Oden

Research output: Contribution to journalArticlepeer-review


A new methodology to build discrete models of boundary-value problems is presented. The h-p cloud method is applicable to arbitrary domains and employs only a scattered set of nodes to build approximate solutions to BVPs. This new method uses radial basis functions of varying size of supports and with polynomial-reproducing properties of arbitrary order. The approximating properties of the h-p cloud functions are investigated in this article and a several theorems concerning these properties are presented. Moving least squares interpolants are used to build a partition of unity on the domain of interest. These functions are then used to construct, at a very low cost, trial and test functions for Galerkin approximations. The method exhibits a very high rate of convergence and has a greater -exibility than traditional h-p finite element methods. Several numerical experiments in 1-D and 2-D are also presented.

Original languageEnglish (US)
Pages (from-to)673-705
Number of pages33
JournalNumerical Methods for Partial Differential Equations
Issue number6
StatePublished - Nov 1996
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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