On principles for the selection of shape functions for the Generalized Finite Element Method

Ivo Babuška, Uday Banerjee, John E. Osborn

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

Effective shape functions for the Generalized Finite Element Method should reflect the available information on the solution. This information is partially fuzzy, because the solution is, of course, unknown, and typically the only available information is the solution's inclusion in a variety of function spaces. It is desirable to choose shape functions that perform robustly over a family of relevant situations. Quantitative notions of robustness are introduced and discussed. We show, in particular, that in one dimension polynomials are robust when the available information consists in inclusions in Sobolev-type spaces that are x-independent.

Original languageEnglish (US)
Pages (from-to)5595-5629
Number of pages35
JournalComputer Methods in Applied Mechanics and Engineering
Volume191
Issue number49-50
DOIs
StatePublished - Dec 6 2002

Keywords

  • Algebraic polynomials
  • Approximations
  • Error estimates
  • Galerkin methods
  • Generalized finite element methods
  • Sup-inf
  • Trigonometric polynomials
  • n-widths

ASJC Scopus subject areas

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

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