A Unified a Posteriori Error Analysis for Discontinuous Galerkin Approximations of Reactive Transport Equations (Journal of Computational Mathematics, 2006)
Four primal discontinuous Galerkin methods are applied to solve reactive transportproblems, namely, Oden-Babuška-Baumann DG (OBB-DG), non-symmetric interior penaltyGalerkin (NIPG), symmetric interior penalty Galerkin (SIPG), and incomplete interiorpenalty Galerkin (IIPG). A unified a posteriori residual-type error estimation is derivedexplicitly 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 foradaptation. Unlike in the reference [10], we obtain the error estimators in $L^2(L^2)$ norm byusing duality techniques instead of in $L^2(H^1)$ norm.