Error estimation for low-order adaptive finite element approximations for fluid flow problems

Alejandro Allendes, Francisco Durán, Richard Rankin

Research output: Journal PublicationArticlepeer-review

5 Citations (Scopus)

Abstract

We derive computable a posteriori error estimates for a wide family of low-order conforming and conforming stabilized finite element approximations for fluid flow problems. The estimators provide upper bounds on the error measured in natural energy-type norms. The analysis combines a Ritz projection of the residuals of the equation with explicit solutions of a local Neumann-type problem which required the introduction of suitable equilibrated fluxes. We provide a general framework in two and three dimensions with explicit formulas, which can be used to implement adaptive procedures. Finally, several numerical experiments are presented to test the performance of the error estimators.

Original languageEnglish
Pages (from-to)1715-1747
Number of pages33
JournalIMA Journal of Numerical Analysis
Volume36
Issue number4
DOIs
Publication statusPublished - 1 Oct 2016
Externally publishedYes

Keywords

  • a posteriori error estimator
  • fluid flow problems
  • stabilized finite element methods

ASJC Scopus subject areas

  • General Mathematics
  • Computational Mathematics
  • Applied Mathematics

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