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Volume 24, Issue 3
A Unified a Posteriori Error Analysis for Discontinuous Galerkin Approximations of Reactive Transport Equations

Ji-Ming Yang & Yan-Ping Chen

J. Comp. Math., 24 (2006), pp. 425-434.

Published online: 2006-06

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  • 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.

  • Keywords

A posteriori error estimates, Duality techniques, Discontinuous Galerkin methods.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-24-425, author = {Ji-Ming Yang and Yan-Ping Chen}, title = {A Unified a Posteriori Error Analysis for Discontinuous Galerkin Approximations of Reactive Transport Equations}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8763.html} }
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 -

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.

Ji-Ming Yang and Yan-Ping Chen. (2006). A Unified a Posteriori Error Analysis for Discontinuous Galerkin Approximations of Reactive Transport Equations. Journal of Computational Mathematics. 24 (3). 425-434. doi:
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