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We develop a general convergence theory for adaptive discontinuous Galerkinmethods for elliptic PDEs covering the popular SIPG, NIPG and LDG schemes aswell as all practically relevant marking strategies. Another key feature of thepresented result is, that it holds for penalty parameters only necessary forthe standard analysis of the respective scheme. The analysis is based on aquasi interpolation into a newly developed limit space of the adaptivelycreated non-conforming discrete spaces, which enables to generalise the basicconvergence result for conforming adaptive finite element methods by Morin,Siebert, and Veeser [A basic convergence result for conforming adaptive finiteelements, Math. Models Methods Appl. Sci., 2008, 18(5), 707--737].

Convergence of adaptive discontinuous Galerkin methods (corrected version of [Math. Comp. 87 (2018), no. 314, 2611--2640])