# Convergence analysis of the lowest order weakly penalized adaptive discontinuous Galerkin methods

Thirupathi Gudi; Johnny Guzmán

- Volume: 48, Issue: 3, page 753-764
- ISSN: 0764-583X

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topGudi, Thirupathi, and 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 48.3 (2014): 753-764. <http://eudml.org/doc/273197>.

@article{Gudi2014,

abstract = {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.},

author = {Gudi, Thirupathi, Guzmán, Johnny},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {contraction; adaptive finite element; discontinuous Galerkin; discontinuous Galerkin method; adaptive finite elements; marking strategy},

language = {eng},

number = {3},

pages = {753-764},

publisher = {EDP-Sciences},

title = {Convergence analysis of the lowest order weakly penalized adaptive discontinuous Galerkin methods},

url = {http://eudml.org/doc/273197},

volume = {48},

year = {2014},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 3

SP - 753

EP - 764

AB - 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.

LA - eng

KW - contraction; adaptive finite element; discontinuous Galerkin; discontinuous Galerkin method; adaptive finite elements; marking strategy

UR - http://eudml.org/doc/273197

ER -

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