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：本文证明，对于$\Real^3$中的一般多面体区域，[Di Pietro和Droniou，多面体网格上任意阶离散de Rham复形：精确性、Poincaré不等式和一致性，Found. Comput. Math.，2021，DOI：\href{https://dx.doi.org/10.1007/s10208-021-09542-8}{10.1007/s10208-021-09542-8}]中离散de Rham复形的上同调空间与连续de Rham复形的上同调空间同构。据我们所知，这是针对由一般多面体网格构建的任意阶复形首次获得此类结果。