Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions

Mark Ainsworth, Alejandro Allendes, Gabriel R. Barrenechea, Richard Rankin

Research output: Journal PublicationArticlepeer-review

23 Citations (Scopus)

Abstract

Fully computable upper bounds are developed for the discretisation error measured in the natural (energy) norm for convection-reaction-diffusion problems in three dimensions. The upper bounds are genuine upper bounds in the sense that the numerical value of the estimated error exceeds the actual numerical value of the true error regardless of the coarseness of the mesh or the nature of the data for the problem. All constants appearing in the bounds are fully specified. Examples show the estimator to be reliable and accurate even in the case of complicated three-dimensional problems.

Original languageEnglish
Pages (from-to)765-790
Number of pages26
JournalInternational Journal for Numerical Methods in Fluids
Volume73
Issue number9
DOIs
Publication statusPublished - 30 Nov 2013
Externally publishedYes

Keywords

  • 3D convection-reaction-diffusion
  • Fully computable a posteriori error estimator
  • SUPG stabilised method

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics

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