A posteriori error estimation and dynamic adaptivity for symmetric discontinuous Galerkin approximations of reactive transport problems

Shuyu Sun*, Mary F. Wheeler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

A symmetric discontinuous Galerkin scheme is applied for solving reactive transport problems. An explicit a posteriori error estimator in L2(L2) is derived for the semi-discrete scheme applied to transport with general kinetic reactions. Explicit a posteriori error estimators in terms of linear functionals and negative norms are also obtained for transport problems with simple reactions. An adaptive approach based on the a posteriori error estimators is proposed to modify the mesh dynamically. Numerical examples demonstrate the efficiency and effectivity of the estimators. Moreover, it is shown in this study that the proposed adaptivity eliminates the need of slope limiters.

Original languageEnglish (US)
Pages (from-to)632-652
Number of pages21
JournalComputer Methods in Applied Mechanics and Engineering
Volume195
Issue number7-8
DOIs
StatePublished - Jan 25 2006
Externally publishedYes

Keywords

  • A posteriori error estimators
  • Adaptivity
  • Discontinuous Galerkin methods
  • SIPG

ASJC Scopus subject areas

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

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