Finite Element Exterior Calculus

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The deal.II finite element library: Design, features, and insights (2019, background): “The publication by Arnold and Logg in [45] and references therein summarizes the most commonly used ones, but there are many others (a subset illustrating the breadth of elements can be found in [46–50]).”
Hodge Laplacians on graphs (2015, background): “” Unlike physical problems arising from areas such as continuum mechanics or electromagnetics, where the differentiable Hodge–de Rham theory has been applied with great efficacy for both modeling and computations [1, 2, 27, 40, 47, 58, 59], those arising from data analytic applications are likely to”
MFEM: a modular finite element methods library (2019, background): “The de Rham complex [34, 35] is a compatible multi-physics discretization framework that naturally connects the solution spaces for many common PDEs.”