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A unified a posteriori error analysis for discontinuous Galerkin approximations of reactive transport equations. (English) Zbl 1142.76034
Summary: We apply four primal discontinuous Galerkin methods to solve reactive transport problems, namely, Oden-Babuška-Baumann, non-symmetric interior penalty Galerkin, symmetric interior penalty Galerkin, and incomplete interior penalty Galerkin. 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 [S. Sun and M. F. Wheeler, J. Sci. Comput. 22, 511–530 (2005; Zbl 1066.76037)], we obtain the error estimators in \(L^2(L^2)\) norm by using duality techniques instead of in \(L^2(H^1)\) norm.

76M10 Finite element methods applied to problems in fluid mechanics
76V05 Reaction effects in flows
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs