The Enriched Crouzeix–Raviart Elements are Equivalent to the Raviart–Thomas Elements

Jun Hu, Rui Ma*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

For both the Poisson model problem and the Stokes problem in any dimension, this paper proves that the enriched Crouzeix–Raviart elements are actually identical to the first order Raviart–Thomas elements in the sense that they produce the same discrete stresses. This result improves the previous result in literature which, for two dimensions, states that the piecewise constant projection of the stress by the first order Raviart–Thomas element is equal to that by the Crouzeix–Raviart element. For the eigenvalue problem of the Laplace operator, this paper proves that the error of the enriched Crouzeix–Raviart element is equivalent to that of the first order Raviart–Thomas element up to higher order terms.

Original languageEnglish
Pages (from-to)410-425
Number of pages16
JournalJournal of Scientific Computing
Volume63
Issue number2
DOIs
Publication statusPublished - 1 May 2015
Externally publishedYes

Keywords

  • Crouzeix–Raviart element
  • Eigenvalue problem
  • Enriched Crouzeix–Raviart element
  • Raviart–Thomas element
  • The Poisson equation
  • The Stokes equation

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