In this article, by my Monash colleague Jerome Droniou, and Daniel A Di Pietro, I am acknowledged for providing an explicit basis for the space \( \mathcal{G}^{c,l} (T) \), which is used in a software implementation.
Di Pietro, Daniele A, Droniou, Jérôme, An arbitrary-order discrete de Rham complex on polyhedral meshes: exactness, Poincaré inequalities, and consistency. Found. Comput. Math. 23 (2023), no.1, 85–164.
The article has open access online and is available here at the journal website.
An Arbitrary-Order Discrete de Rham Complex on Polyhedral Meshes