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In this article, we prove convergence of the weakly penalized adaptive discontinuous Galerkin methods. Unlike other works, we derive the contraction property for various discontinuous Galerkin methods only assuming the stabilizing parameters are large enough to stabilize the method. A central idea in the analysis is to construct an auxiliary solution from the discontinuous Galerkin solution by a simple post processing. Based on the auxiliary solution, we define the adaptive algorithm which guides to the convergence of adaptive discontinuous Galerkin methods.
@article{M2AN_2014__48_3_753_0,
author = {Gudi, Thirupathi and Guzm\'an, Johnny},
title = {Convergence analysis of the lowest order weakly penalized adaptive discontinuous {Galerkin} methods},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {753--764},
publisher = {EDP-Sciences},
volume = {48},
number = {3},
year = {2014},
doi = {10.1051/m2an/2013119},
mrnumber = {3264333},
zbl = {1298.65174},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013119/}
}
TY - JOUR AU - Gudi, Thirupathi AU - Guzmán, Johnny TI - Convergence analysis of the lowest order weakly penalized adaptive discontinuous Galerkin methods JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 753 EP - 764 VL - 48 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013119/ DO - 10.1051/m2an/2013119 LA - en ID - M2AN_2014__48_3_753_0 ER -
%0 Journal Article %A Gudi, Thirupathi %A Guzmán, Johnny %T Convergence analysis of the lowest order weakly penalized adaptive discontinuous Galerkin methods %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 753-764 %V 48 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013119/ %R 10.1051/m2an/2013119 %G en %F M2AN_2014__48_3_753_0
Gudi, Thirupathi; Guzmán, Johnny. Convergence analysis of the lowest order weakly penalized adaptive discontinuous Galerkin methods. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 3, pp. 753-764. doi: 10.1051/m2an/2013119
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