An exterior calculus framework for polytopal methods - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2023

An exterior calculus framework for polytopal methods


We develop in this work the first polytopal complexes of differential forms. These complexes, inspired by the Discrete De Rham and the Virtual Element approaches, are discrete versions of the de Rham complex of differential forms built on meshes made of general polytopal elements. Both constructions benefit from the high-level approach of polytopal methods, which leads, on certain meshes, to leaner constructions than the finite element method. We establish commutation properties between the interpolators and the discrete and continuous exterior derivatives, prove key polynomial consistency results for the complexes, and show that their cohomologies are isomorphic to the cohomology of the continuous de Rham complex.
Fichier principal
Vignette du fichier
ddr-pec.pdf (466.79 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-04037653 , version 1 (20-03-2023)



Francesco Bonaldi, Daniele A. Di Pietro, Jérôme Droniou, Kaibo Hu. An exterior calculus framework for polytopal methods. 2023. ⟨hal-04037653⟩
27 View
16 Download



Gmail Facebook Twitter LinkedIn More