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Volume 9, Issue 1
Convergence and Quasi-Optimality of an Adaptive Multi-Penalty Discontinuous Galerkin Method

Zhenhua Zhou & Haijun Wu

DOI: 10.4208/nmtma.2015.m1412

Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 51-86.

Published online: 2016-09

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  • Abstract

An adaptive multi-penalty discontinuous Galerkin method (AMPDG) for the diffusion problem is considered. Convergence and quasi-optimality of the AMPDG are proved. Compared with the analyses for the adaptive finite element method or the adaptive interior penalty discontinuous Galerkin method, extra works is done to overcome the difficulties caused by the additional penalty terms.

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@Article{NMTMA-9-51, author = {}, title = {Convergence and Quasi-Optimality of an Adaptive Multi-Penalty Discontinuous Galerkin Method}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2016}, volume = {9}, number = {1}, pages = {51--86}, abstract = {

An adaptive multi-penalty discontinuous Galerkin method (AMPDG) for the diffusion problem is considered. Convergence and quasi-optimality of the AMPDG are proved. Compared with the analyses for the adaptive finite element method or the adaptive interior penalty discontinuous Galerkin method, extra works is done to overcome the difficulties caused by the additional penalty terms.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.m1412}, url = {http://global-sci.org/intro/article_detail/nmtma/12367.html} }
TY - JOUR T1 - Convergence and Quasi-Optimality of an Adaptive Multi-Penalty Discontinuous Galerkin Method JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 51 EP - 86 PY - 2016 DA - 2016/09 SN - 9 DO - http://doi.org/10.4208/nmtma.2015.m1412 UR - https://global-sci.org/intro/article_detail/nmtma/12367.html KW - AB -

An adaptive multi-penalty discontinuous Galerkin method (AMPDG) for the diffusion problem is considered. Convergence and quasi-optimality of the AMPDG are proved. Compared with the analyses for the adaptive finite element method or the adaptive interior penalty discontinuous Galerkin method, extra works is done to overcome the difficulties caused by the additional penalty terms.

Zhenhua Zhou & Haijun Wu. (2020). Convergence and Quasi-Optimality of an Adaptive Multi-Penalty Discontinuous Galerkin Method. Numerical Mathematics: Theory, Methods and Applications. 9 (1). 51-86. doi:10.4208/nmtma.2015.m1412
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