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

Daniele A. Di Pietro; Jérôme Droniou; Silvano Pitassi

doi:10.1007/s10092-023-00523-7

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

Daniele A. Di Pietro, Jérôme Droniou, Silvano Pitassi

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

4 Citations (Scopus)

Abstract

In this work we prove that, for a general polyhedral domain of R³ , the cohomology spaces of the discrete de Rham complex of Di Pietro and Droniou (Found Comput Math 23:85–164, 2023, https://doi.org/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 a fully computable arbitrary-order complex built from a general polyhedral mesh.

Original language	English
Article number	32
Number of pages	25
Journal	Calcolo
Volume	60
Issue number	2
DOIs	https://doi.org/10.1007/s10092-023-00523-7
Publication status	Published - Jun 2023

Keywords

Cohomology
Compatible discretisations
Discrete de Rham method
Polytopal methods

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10.1007/s10092-023-00523-7Licence: CC BY

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title = "Cohomology of the discrete de Rham complex on domains of general topology",

abstract = "In this work we prove that, for a general polyhedral domain of R3 , the cohomology spaces of the discrete de Rham complex of Di Pietro and Droniou (Found Comput Math 23:85–164, 2023, https://doi.org/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 a fully computable arbitrary-order complex built from a general polyhedral mesh.",

keywords = "Cohomology, Compatible discretisations, Discrete de Rham method, Polytopal methods",

author = "\{Di Pietro\}, \{Daniele A.\} and J{\'e}r{\^o}me Droniou and Silvano Pitassi",

note = "Funding Information: The authors acknowledge the partial support of Agence Nationale de la Recherche grant ANR-20-MRS2-0004 NEMESIS. Daniele Di Pietro also acknowledges the partial support of I-Site MUSE grant ANR-16-IDEX-0006 RHAMNUS. J{\'e}r{\^o}me Droniou was partially supported by the Australian Research Council through the Discovery Projects funding scheme (Project No. DP210103092). Publisher Copyright: {\textcopyright} 2023, Crown.",

year = "2023",

month = jun,

doi = "10.1007/s10092-023-00523-7",

language = "English",

volume = "60",

journal = "Calcolo",

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T1 - Cohomology of the discrete de Rham complex on domains of general topology

AU - Di Pietro, Daniele A.

AU - Droniou, Jérôme

AU - Pitassi, Silvano

N1 - Funding Information: The authors acknowledge the partial support of Agence Nationale de la Recherche grant ANR-20-MRS2-0004 NEMESIS. Daniele Di Pietro also acknowledges the partial support of I-Site MUSE grant ANR-16-IDEX-0006 RHAMNUS. Jérôme Droniou was partially supported by the Australian Research Council through the Discovery Projects funding scheme (Project No. DP210103092). Publisher Copyright: © 2023, Crown.

PY - 2023/6

Y1 - 2023/6

N2 - In this work we prove that, for a general polyhedral domain of R3 , the cohomology spaces of the discrete de Rham complex of Di Pietro and Droniou (Found Comput Math 23:85–164, 2023, https://doi.org/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 a fully computable arbitrary-order complex built from a general polyhedral mesh.

AB - In this work we prove that, for a general polyhedral domain of R3 , the cohomology spaces of the discrete de Rham complex of Di Pietro and Droniou (Found Comput Math 23:85–164, 2023, https://doi.org/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 a fully computable arbitrary-order complex built from a general polyhedral mesh.

KW - Cohomology

KW - Compatible discretisations

KW - Discrete de Rham method

KW - Polytopal methods

UR - https://www.scopus.com/pages/publications/85160081313

U2 - 10.1007/s10092-023-00523-7

DO - 10.1007/s10092-023-00523-7

M3 - Article

AN - SCOPUS:85160081313

SN - 0008-0624

VL - 60

JO - Calcolo

JF - Calcolo

IS - 2

M1 - 32

ER -

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

Abstract

Keywords

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