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

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  15 February 2016

Zhenhua Zhou  and
Haijun Wu
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
*
*Corresponding author. Email addresses: njuzzh@gmail.com (Z.-H. Zhou Zhou), hjw@nju.edu.cn (H.-J. Wu)
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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.

Keywords

Multi-penalty discontinuous Galerkin methodadaptive algorithmconvergencequasi-optimality

MSC classification

Secondary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N12: Stability and convergence of numerical methods
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 1 , February 2016 , pp. 51 - 86
Copyright
Copyright © Global-Science Press 2016 

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