P-Adaptive C k generalized finite element method for arbitrary polygonal clouds

Felício B. Barros, Clovis S. De Barcellos, Carlos A. Duarte

Research output: Contribution to journalArticlepeer-review


A p-Adaptive Generalized Finite Element Method (GFEM) based on a Partition of Unity (POU) of arbitrary smoothness degree is presented. The shape functions are built from the product of a Shepard POU and enrichment functions. Shepard functions have a smoothness degree directly related to the weighting functions adopted in their definition. Here the weighting functions are obtained from boolean R-functions which allow the construction of C k approximations, with k arbitrarily large, defined over a polygonal patch of elements, named cloud. The Element Residual Method is used to obtain error indicators by taking into account the typical nodal enrichment scheme of the method. This procedure is enhanced by using approximations with a high degree of smoothness as it eliminates the discontinuity of the stress field in the interior of each cloud. Adaptive analysis of plane elasticity problems are presented, and the performance of the technique is investigated.

Original languageEnglish (US)
Pages (from-to)175-187
Number of pages13
JournalComputational Mechanics
Issue number1
StatePublished - Dec 2007


  • Adaptivity
  • Error estimator
  • Generalized finite element method
  • Mesh reduction methods
  • Partition of unity

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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