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

Jérôme Droniou
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Silvano Pitassi
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Abstract

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, Poincaré 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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Dates and versions

hal-03767946 , version 1 (02-09-2022)

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  • HAL Id : hal-03767946 , version 1

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Daniele Antonio Di Pietro, Jérôme Droniou, Silvano Pitassi. Cohomology of the discrete de Rham complex on domains of general topology. 2022. ⟨hal-03767946⟩
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