Convergence of adaptive discontinuous galerkin methods
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Date
2017-08
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Abstract
We develop a general convergence theory for adaptive discontinu-
ous Galerkin methods for elliptic PDEs covering the popular SIPG, NIPG and
LDG schemes as well as all practically relevant marking strategies. Another
key feature of the presented result is, that it holds for penalty parameters only
necessary for the standard analysis of the respective scheme. The analysis
is based on a quasi interpolation into a newly developed limit space of the
adaptively created non-conforming discrete spaces, which enables to generalise
the basic convergence result for conforming adaptive finite element methods by
Morin, Siebert, and Veeser [A basic convergence result for conforming adaptive
finite elements, Math. Models Methods Appl. Sci., 2008, 18(5), 707–737].