Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains

Yi Zhang; Varun Jain; Artur Palha; Marc Gerritsma

doi:10.1007/978-3-030-39647-3_15

Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains

Yi Zhang^*, Varun Jain, Artur Palha, Marc Gerritsma

^*Corresponding author for this work

Aerodynamics

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

In this paper, we will show that the equivalence of a div-grad Neumann problem and a grad-div Dirichlet problem can be preserved at the discrete level in 3-dimensional curvilinear domains if algebraic dual polynomial representations are employed. These representations will be introduced. Proof of the equivalence at the discrete level follows from the construction of the algebraic dual representations. A 3-dimensional test problem in curvilinear coordinates will illustrate this approach.

Original language	English
Title of host publication	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference
Editors	Spencer J. Sherwin, Joaquim Peiró, Peter E. Vincent, David Moxey, Christoph Schwab
Publisher	SpringerOpen
Pages	203-213
Number of pages	11
ISBN (Print)	9783030396466
DOIs	https://doi.org/10.1007/978-3-030-39647-3_15
Publication status	Published - 2020
Event	12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018 - London, United Kingdom Duration: 9 Jul 2018 → 13 Jul 2018

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	134
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018
Country/Territory	United Kingdom
City	London
Period	9/07/18 → 13/07/18

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10.1007/978-3-030-39647-3_15

Zhang2020_Chapter_DiscreteEquivalenceOfAdjointNeFinal published version, 324 KB

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Zhang, Y., Jain, V., Palha, A., & Gerritsma, M. (2020). Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains. In S. J. Sherwin, J. Peiró, P. E. Vincent, D. Moxey, & C. Schwab (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference (pp. 203-213). (Lecture Notes in Computational Science and Engineering; Vol. 134). SpringerOpen. https://doi.org/10.1007/978-3-030-39647-3_15

Zhang, Yi ; Jain, Varun ; Palha, Artur et al. / Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. editor / Spencer J. Sherwin ; Joaquim Peiró ; Peter E. Vincent ; David Moxey ; Christoph Schwab. SpringerOpen, 2020. pp. 203-213 (Lecture Notes in Computational Science and Engineering).

@inproceedings{7c6934d8794040e39aeba992cdd83c04,

title = "Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains",

abstract = "In this paper, we will show that the equivalence of a div-grad Neumann problem and a grad-div Dirichlet problem can be preserved at the discrete level in 3-dimensional curvilinear domains if algebraic dual polynomial representations are employed. These representations will be introduced. Proof of the equivalence at the discrete level follows from the construction of the algebraic dual representations. A 3-dimensional test problem in curvilinear coordinates will illustrate this approach.",

author = "Yi Zhang and Varun Jain and Artur Palha and Marc Gerritsma",

year = "2020",

doi = "10.1007/978-3-030-39647-3_15",

language = "English",

isbn = "9783030396466",

series = "Lecture Notes in Computational Science and Engineering",

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editor = "Sherwin, {Spencer J.} and Joaquim Peir{\'o} and Vincent, {Peter E.} and David Moxey and Christoph Schwab",

booktitle = "Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference",

note = "12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018 ; Conference date: 09-07-2018 Through 13-07-2018",

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Zhang, Y, Jain, V , Palha, A & Gerritsma, M 2020, Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains. in SJ Sherwin, J Peiró, PE Vincent, D Moxey & C Schwab (eds), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. Lecture Notes in Computational Science and Engineering, vol. 134, SpringerOpen, pp. 203-213, 12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018, London, United Kingdom, 9/07/18. https://doi.org/10.1007/978-3-030-39647-3_15

Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains. / Zhang, Yi; Jain, Varun ; Palha, Artur et al.
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. ed. / Spencer J. Sherwin; Joaquim Peiró; Peter E. Vincent; David Moxey; Christoph Schwab. SpringerOpen, 2020. p. 203-213 (Lecture Notes in Computational Science and Engineering; Vol. 134).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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T1 - Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains

AU - Zhang, Yi

AU - Jain, Varun

AU - Palha, Artur

AU - Gerritsma, Marc

PY - 2020

Y1 - 2020

N2 - In this paper, we will show that the equivalence of a div-grad Neumann problem and a grad-div Dirichlet problem can be preserved at the discrete level in 3-dimensional curvilinear domains if algebraic dual polynomial representations are employed. These representations will be introduced. Proof of the equivalence at the discrete level follows from the construction of the algebraic dual representations. A 3-dimensional test problem in curvilinear coordinates will illustrate this approach.

AB - In this paper, we will show that the equivalence of a div-grad Neumann problem and a grad-div Dirichlet problem can be preserved at the discrete level in 3-dimensional curvilinear domains if algebraic dual polynomial representations are employed. These representations will be introduced. Proof of the equivalence at the discrete level follows from the construction of the algebraic dual representations. A 3-dimensional test problem in curvilinear coordinates will illustrate this approach.

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DO - 10.1007/978-3-030-39647-3_15

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AN - SCOPUS:85089722337

SN - 9783030396466

T3 - Lecture Notes in Computational Science and Engineering

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BT - Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference

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A2 - Peiró, Joaquim

A2 - Vincent, Peter E.

A2 - Moxey, David

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PB - SpringerOpen

T2 - 12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018

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Zhang Y, Jain V , Palha A , Gerritsma M. Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains. In Sherwin SJ, Peiró J, Vincent PE, Moxey D, Schwab C, editors, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. SpringerOpen. 2020. p. 203-213. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-030-39647-3_15

Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains

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