Symmetric and nonsymmetric discontinuous galerkin methods for reactive transport in porous media

Shuyu Sun*, Mary F. Wheeler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

123 Scopus citations

Abstract

For solving reactive transport problems in porous media, we analyze three primal discontinuous Galerkin (DG) methods with penalty, namely, symmetric interior penalty Galerkin (SIPG), nonsymmetric interior penalty Galerkin (NIPG), and incomplete interior penalty Galerkin (IIPG). A cut-off operator is introduced in DG to treat general kinetic chemistry. Error estimates in L 2(H 1) are established, which are optimal in h and nearly optimal in p. We develop a parabolic lift technique for SIPG, which leads to h-optimal and nearly p-optimal error estimates in the L 2(L 2) and negative norms. Numerical results validate these estimates. We also discuss implementation issues including penalty parameters and the choice of physical versus reference polynomial spaces.

Original languageEnglish (US)
Pages (from-to)195-219
Number of pages25
JournalSIAM Journal on Numerical Analysis
Volume43
Issue number1
DOIs
StatePublished - Dec 1 2005

Keywords

  • Discontinuous Galerkin methods
  • Error estimates
  • IIPG
  • NIPG
  • Parabolic partial differential equations
  • Porous media
  • Reactive transport
  • SIPG

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Symmetric and nonsymmetric discontinuous galerkin methods for reactive transport in porous media'. Together they form a unique fingerprint.

Cite this