Multigrid in H (div) and H (curl)

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Finite Element Methods for Maxwell's Equations (2019, background): “The recognition by Bossavit [11] (see also [31]) that this, and a similar equality for H(curl; Ω) and H(div; Ω) interpolation, constitute a discrete de Rham complex motivated in part the Finite Element Exterior Calculus of Arnold, Falk and Winther [3, 2].”
Finite element exterior calculus, homological techniques, and applications (2006, methodology): “We refer to Arnold et al. (2000) for further details.”
High order Nédélec elements with local complete sequence properties (2005, background): “Also the kernelpreserving multigrid preconditioners of [7], [8] are based on the knowledge of the curl-free functions.”
Mixed finite element methods for incompressible flow: Stationary Stokes equations (2010, methodology): “, [20]) that the form Bε(·, ·) can be efficiently preconditioned by the multigrid (V-cycle) preconditioner with appropriate additive or multiplicative Schwarz smoothers.”
ROBUST SUBSPACE CORRECTION METHODS FOR NEARLY SINGULAR SYSTEMS (2007, unknown): “For simplicity, we only consider the vertex-base decomposition [ 2 ].”
A family of nonconforming elements for the Brinkman problem (2012, unknown): “We will need the following well known result ([33, 32, 3, 2]) that says that the following is an exact discrete complex: R ⊂ −→ Lh grad −→ Nh curl −→ Mh div −→ Wh −→ 0, (6.”