Corrigendum to ''Convergence of adaptive, discontinuous Galerkin methods''.

The first statement of Lemma 11 in our recent paper [KG18] (Math. Comp. 87 (2018), no. 314, 2611-2640) is incorrect: For the sequence {Gk}k of nested admissible partitions produced by the adaptive discontinuous Galerkin method (ADGM) we have G+ := ∪k≥0∩j≥kGj, and Ω+ := (∪ E: E ∈ G+}). In the first line of the proof of [KG18, Lemma 11 on p. 2620], we used that |Ω| = |interior(Ω\Ω+)| + |Ω+|, where \vert\cdot \vert denotes the Lebesgue measure. This, however, is not true in general, since there are counter examples where Ω+ is dense in Ω and 0 = |interior(Ω\Ω+)| < |Ω\Ω+| 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. [ABSTRACT FROM AUTHOR]