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Convergence analysis of the lowest order weakly penalizedadaptive discontinuous Galerkin methods

Published online by Cambridge University Press:  01 April 2014

Thirupathi Gudi  and
Johnny Guzmán
Thirupathi Gudi
Affiliation:
Department of Mathematics, Indian Institute of Science, 56002 Bangalore, India.. gudi@math.iisc.ernet.in
Johnny Guzmán
Affiliation:
Division of Applied Mathematics, Brown University, Providence, 02912 RI, USA.; JohnnyGuzman@brown.edu
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Abstract

In this article, we prove convergence of the weakly penalized adaptive discontinuousGalerkin methods. Unlike other works, we derive the contraction property for variousdiscontinuous Galerkin methods only assuming the stabilizing parameters are large enoughto stabilize the method. A central idea in the analysis is to construct an auxiliarysolution from the discontinuous Galerkin solution by a simple post processing. Based onthe auxiliary solution, we define the adaptive algorithm which guides to the convergenceof adaptive discontinuous Galerkin methods.

Keywords

Contractionadaptive finite elementdiscontinuous Galerkin

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 3 , May 2014 , pp. 753 - 764
Copyright
© EDP Sciences, SMAI 2014

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