TY - JOUR
T1 - A Unified a Posteriori Error Analysis for Discontinuous Galerkin Approximations of Reactive Transport Equations
AU - Ji-Ming Yang & Yan-Ping Chen
JO - Journal of Computational Mathematics
VL - 3
SP - 425
EP - 434
PY - 2006
DA - 2006/06
SN - 24
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8763.html
KW - A posteriori error estimates, Duality techniques, Discontinuous Galerkin methods.
AB - <p style="text-align: justify;">Four primal discontinuous Galerkin methods are applied to solve reactive transport
problems, namely, Oden-Babuška-Baumann DG (OBB-DG), non-symmetric interior penalty
Galerkin (NIPG), symmetric interior penalty Galerkin (SIPG), and incomplete interior
penalty Galerkin (IIPG). A unified a posteriori residual-type error estimation is derived
explicitly for these methods. From the computed solution and given data, explicit estimators can be computed efficiently and directly, which can be used as error indicators for
adaptation. Unlike in the reference [10], we obtain the error estimators in $L^2(L^2)$ norm by
using duality techniques instead of in $L^2(H^1)$ norm.</p>