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arXiv · 2209.00957

Cohomology of the discrete de Rham complex on domains of general topology

Daniele A. Di Pietro·Jérôme Droniou·Silvano Pitassi
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Abstract

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.

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Daniele A. Di Pietro, Jérôme Droniou, Silvano Pitassi. 2022-09-02. Cohomology of the discrete de Rham complex on domains of general topology. https://doi.org/10.1007/s10092-023-00523-7

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