A Unified a Posteriori Error Analysis for Discontinuous Galerkin Approximations of Reactive Transport Equations
Year: 2006
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 3 : pp. 425–434
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-JCM-8763
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 3 : pp. 425–434
Published online: 2006-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: A posteriori error estimates Duality techniques Discontinuous Galerkin methods.