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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Corrigendum to “Convergence of adaptive, discontinuous Galerkin methods”
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by Christian Kreuzer and Emmanuil H. Georgoulis HTML | PDF
Math. Comp. 90 (2021), 637-640 Request permission


The first statement of Lemma 11 in our recent paper [KG18] (Math. Comp. 87 (2018), no. 314, 2611–2640) is incorrect: For the sequence $\{\mathcal {G}_{k}\}_k$ of nested admissible partitions produced by the adaptive discontinuous Galerkin method (ADGM) we have $\mathcal {G}^+\coloneq \bigcup _{k\ge 0}\bigcap _{j\ge k}\mathcal {G}_{j}$, and $\Omega ^+\coloneq \operatorname {interior}\left (\bigcup \{ E: E\in \mathcal {G}^+\}\right )$. In the first line of the proof of [KG18, Lemma 11 on p. 2620], we used that \begin{align*} |\Omega |=|\operatorname {interior}(\Omega \setminus \Omega ^+)|+|\Omega ^+|, \end{align*} where $|\cdot |$ denotes the Lebesgue measure. This, however, is not true in general, since there are counter examples where $\Omega ^+$ is dense in $\Omega$ and \[ 0=|\operatorname {interior}(\Omega \setminus \Omega ^+)|<|\Omega \setminus \Omega ^+|. \]

Below, we present the required minor modifications to complete the proof of the main result stating convergence of the ADGM of [KG18] and address some typos regarding the broken dG-norm. A corrected full version of the article is available at arXiv:1909.12665v2.

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Additional Information
  • Christian Kreuzer
  • Affiliation: Fakultät für Mathematik, Technische Universität Dortmund, Vogelpothsweg 87, D-44227 Dortmund, Germany
  • MR Author ID: 833122
  • ORCID: 0000-0003-2923-4428
  • Email:
  • Emmanuil H. Georgoulis
  • Affiliation: Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom; and Department of Mathematics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Zografou 157 80, Greece
  • MR Author ID: 750860
  • Email:
  • Received by editor(s): October 1, 2019
  • Received by editor(s) in revised form: September 8, 2020
  • Published electronically: December 21, 2020
  • Additional Notes: The research of the first author was supported by DFG research grant KR 3984/5-1.
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 90 (2021), 637-640
  • MSC (2020): Primary 65N30, 65N12, 65N50, 65N15
  • DOI:
  • MathSciNet review: 4194157