L2(H1 norm a posteriori error estimation for discontinuous Galerkin approximations of reactive transport problems

Shuyu Sun*, Mary F. Wheeler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

66 Scopus citations

Abstract

Explicita posteriori residual type error estimators in L2(H 1) norm are derived for discontinuous Galerkin (DG) methods applied to transport in porous media with general kinetic reactions. They are flexible and apply to all the four primal DG schemes, namely, Oden-Babuška-Baumann DG (OBB-DG), non-symmetric interior penalty Galerkin (NIPG), symmetric interior penalty Galerkin (SIPG) and incomplete interior penalty Galerkin (IIPG). The error estimators use directly all the available information from the numerical solution and can be computed efficiently. Numerical examples are presented to demonstrate the efficiency and the effectivity of these theoretical estimators.

Original languageEnglish (US)
Pages (from-to)501-530
Number of pages30
JournalJournal of Scientific Computing
Volume22-23
DOIs
StatePublished - Jan 1 2005

Keywords

  • A posteriori error estimators
  • Discontinuous Galerkin methods
  • Hp adaptivity
  • IIPG
  • NIPG
  • OBB-DG
  • SIPG

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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