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Convergence and Quasi-Optimality of an Adaptive Multi-Penalty Discontinuous Galerkin Method

Published online by Cambridge University Press:  15 February 2016

Zhenhua Zhou
Affiliation:
Department of Mathematics, Nanjing University, Jiangsu, 210093, P. R. China
Haijun Wu
Affiliation:
Department of Mathematics, Nanjing University, Jiangsu, 210093, P. R. China
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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 are done to overcome the difficulties caused by the additional penalty terms.

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Research Article
Copyright
Copyright © Global-Science Press 2016 

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Convergence and Quasi-Optimality of an Adaptive Multi-Penalty Discontinuous Galerkin Method
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