Symmetric and Nonsymmetric Discontinuous Galerkin Methods for Reactive Transport in Porous Media

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 L2(H1) 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 L2(L2) 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.