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Convergence of adaptive discontinuous Galerkin methods

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journal contribution
posted on 26.11.2020, 16:32 by C Kreuzer, EH Georgoulis
We develop a general convergence theory for adaptive discontinuous 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 us to generalise the basic convergence result for conforming adaptive finite element methods by Morin, Siebert, and Veeser.

History

Citation

Math. Comp. 87 (2018), 2611-2640

Author affiliation

School of Mathematics & Actuarial Science

Version

AM (Accepted Manuscript)

Published in

Mathematics of Computation

Volume

87

Issue

314

Pagination

2611 - 2640

Publisher

American Mathematical Society (AMS)

issn

0025-5718

eissn

1088-6842

Copyright date

2018

Language

en

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