Convergence analysis of the lowest order weakly penalized adaptive discontinuous Galerkin methods
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 3, p. 753-764
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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.

DOI : https://doi.org/10.1051/m2an/2013119
Classification:  65N30,  65N15
Keywords: contraction, adaptive finite element, discontinuous Galerkin
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {3},
     year = {2014},
     pages = {753-764},
     doi = {10.1051/m2an/2013119},
     zbl = {1298.65174},
     mrnumber = {3264333},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 3, pp. 753-764. doi : 10.1051/m2an/2013119. http://www.numdam.org/item/M2AN_2014__48_3_753_0/

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