Approximation properties of the Generalized Finite Element Method

C. Anitescu, U. Banerjee

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

In this paper, we have obtained an approximation result in the Generalized Finite Element Method (GFEM) that reflects the global approximation property of the Partition of Unity (PU) as well as the approximability of the local approximation spaces. We have considered a GFEM, where the underlying PU functions reproduce polynomials of degree l. With the space of polynomials of degree k serving as the local approximation spaces of the GFEM, we have shown, in particular, that the energy norm of the GFEM approximation error of a smooth function is O(hl+k). This result cannot be obtained from the classical approximation result of GFEM, which does not reflect the global approximation property of the PU.

Original languageEnglish (US)
Pages (from-to)369-390
Number of pages22
JournalAdvances in Computational Mathematics
Volume34
Issue number4
DOIs
StatePublished - May 1 2011

Keywords

  • Approximation
  • Error estimates
  • Generalized finite element method
  • Partition of unity
  • Quasi-interpolation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Approximation properties of the Generalized Finite Element Method'. Together they form a unique fingerprint.

  • Cite this