Convergence of Multigrid Algorithms for Interior Penalty Methods

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Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations ofElliptic Problems (2007, methodology): “Furthermore, due to the close relation between multiplicative Schwarz and multigrid methods [38,41] (both are product type iterative methods), the construction and analysis presented here might throw some new light in the research of multigrid preconditioners for DG approximations, a field where few”
hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes (2016, unknown): “Also, powerful solvers are now available for the resulting linear systems; indeed, both domain decomposition preconditioners, see, for example, [1, 2, 4, 5, 29, 39], and the references cited therein, as well as multigrid solvers, cf. [6,7,17,18], have been developed.”
Forty Years of the Crouzeix‐Raviart element (2015, result): “The results in [104] have since been extended to other nonconforming methods and DG methods [92, 95, 106].”
Multigrid for an HDG method (2013, methodology): “Under the same assumption, multigrid for DG methods were considered in (Brenner & Zhao, 2005; Duan et al., 2007).”