In this work we prove that, for a general polyhedral domain of $\Real^3$, 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: \href{https://dx.doi.org/10.1007/s10208-021-09542-8}{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.

翻译：在这项工作中,我们证明,对于3美元的一般多元域而言,[Di Pietro和Droniou,一个在多面体上的任意离散的Rham综合体:准确性、poincar\'e不平等和一致性,Found.Comput. Math.,2021,DOI:\href{https://dx.doi.org/10.1007/s102008-021-021-09542-8 ⁇ 10.1007/S1008-0208-09542-8 ⁇ 10.1008-021-021-0542-8 ⁇ 10.s1008-021-091-09542-8}]的离散地体群与连续的Rham综合体是无形态的。 据我们所知,这是从一个一般性的多面体中建立的任意综合体综合体的首个结果。