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 language | English (US) |
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Pages (from-to) | 195-219 |
Number of pages | 25 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 43 |
Issue number | 1 |
DOIs | |
State | Published - 2005 |
Externally published | Yes |
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