  In this work we prove that, for a general polyhedral domain of
$\mathbb{R}^3$, the cohomology spaces of the discrete de Rham complex of [Di
Pietro and Droniou, An arbitrary-order discrete de Rham complex on polyhedral
meshes: Exactness, Poincar\'e inequalities, and consistency, Found. Comput.
Math., 2021, DOI: 10.1007/s10208-021-09542-8] are isomorphic to those of the
continuous de Rham complex. This is, to the best of our knowledge, the first
result of this kind for an arbitrary-order complex built from a general
polyhedral mesh.

Numerical Analysis;Numerical Analysis