A decomposition of the raviart-thomas finite element into a scalar and an orientation-preserving part

Fleurianne Bertrand

doi:10.23967/wccm-eccomas.2020.034

A decomposition of the raviart-thomas finite element into a scalar and an orientation-preserving part

Fleurianne Bertrand^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

This contribution considers the conforming finite element discretizations the vector-valued function space H(div, Ω) in 2 and 3 dimensions. A new set of basis functions on simplices is introduced, using a decomposition into an orientation setting part with the edgewise constant normal flux as a degree of freedom and an orientation preserving higher-order part. As a simple combination of lowest-order Raviart-Thomas elements and higher order Lagrange-elements, the basis is suited for fast assembling strategies.

Original language	English
Title of host publication	14th World Congress on Computational Mechanics
Subtitle of host publication	WCCM-ECCOMAS Congress 2020
Editors	F. Chinesta, R. Abgrall, O. Allix, M. Kaliske
Publisher	SCIPEDIA
Number of pages	12
Volume	2100
DOIs	https://doi.org/10.23967/wccm-eccomas.2020.034
Publication status	Published - 10 Mar 2021
Event	14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020 - Virtual, Online Duration: 11 Jan 2021 → 15 Jan 2021

Conference

Conference	14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020
Abbreviated title	WCCM-ECCOMAS 2020
Period	11/01/21 → 15/01/21

Keywords

Mixed finite element methods
Raviart-Thomas element

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10.23967/wccm-eccomas.2020.034Licence: CC BY-NC-SA

A decompositionFinal published version, 263 KBLicence: CC BY-NC-SA

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title = "A decomposition of the raviart-thomas finite element into a scalar and an orientation-preserving part",

abstract = "This contribution considers the conforming finite element discretizations the vector-valued function space H(div, Ω) in 2 and 3 dimensions. A new set of basis functions on simplices is introduced, using a decomposition into an orientation setting part with the edgewise constant normal flux as a degree of freedom and an orientation preserving higher-order part. As a simple combination of lowest-order Raviart-Thomas elements and higher order Lagrange-elements, the basis is suited for fast assembling strategies.",

keywords = "Mixed finite element methods, Raviart-Thomas element",

author = "Fleurianne Bertrand",

note = "Funding Information: 1Acknowledgments: The author gratefully acknowledge support by the Deutsche Forschungsgemeinschaft in the Priority Program SPP 1748 Reliable simulation techniques in solid mechanics, Development of non standard discretization methods, mechanical and mathematical analysis under the project number BE 6511/1-1. Publisher Copyright: {\textcopyright} 2021, Scipedia S.L. All rights reserved.; 14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020, WCCM-ECCOMAS 2020 ; Conference date: 11-01-2021 Through 15-01-2021",

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doi = "10.23967/wccm-eccomas.2020.034",

language = "English",

volume = "2100",

editor = "F. Chinesta and R. Abgrall and O. Allix and M. Kaliske",

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Bertrand, F 2021, A decomposition of the raviart-thomas finite element into a scalar and an orientation-preserving part. in F Chinesta, R Abgrall, O Allix & M Kaliske (eds), 14th World Congress on Computational Mechanics: WCCM-ECCOMAS Congress 2020. vol. 2100, SCIPEDIA, 14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020, 11/01/21. https://doi.org/10.23967/wccm-eccomas.2020.034

A decomposition of the raviart-thomas finite element into a scalar and an orientation-preserving part. / Bertrand, Fleurianne.
14th World Congress on Computational Mechanics: WCCM-ECCOMAS Congress 2020. ed. / F. Chinesta; R. Abgrall; O. Allix; M. Kaliske. Vol. 2100 SCIPEDIA, 2021.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N1 - Funding Information: 1Acknowledgments: The author gratefully acknowledge support by the Deutsche Forschungsgemeinschaft in the Priority Program SPP 1748 Reliable simulation techniques in solid mechanics, Development of non standard discretization methods, mechanical and mathematical analysis under the project number BE 6511/1-1. Publisher Copyright: © 2021, Scipedia S.L. All rights reserved.

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N2 - This contribution considers the conforming finite element discretizations the vector-valued function space H(div, Ω) in 2 and 3 dimensions. A new set of basis functions on simplices is introduced, using a decomposition into an orientation setting part with the edgewise constant normal flux as a degree of freedom and an orientation preserving higher-order part. As a simple combination of lowest-order Raviart-Thomas elements and higher order Lagrange-elements, the basis is suited for fast assembling strategies.

AB - This contribution considers the conforming finite element discretizations the vector-valued function space H(div, Ω) in 2 and 3 dimensions. A new set of basis functions on simplices is introduced, using a decomposition into an orientation setting part with the edgewise constant normal flux as a degree of freedom and an orientation preserving higher-order part. As a simple combination of lowest-order Raviart-Thomas elements and higher order Lagrange-elements, the basis is suited for fast assembling strategies.

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A2 - Allix, O.

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A decomposition of the raviart-thomas finite element into a scalar and an orientation-preserving part

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