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

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

1 Citation (Scopus)
7 Downloads (Pure)

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 languageEnglish
Title of host publicationSpectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference
EditorsSpencer J. Sherwin, Joaquim Peiró, Peter E. Vincent, David Moxey, Christoph Schwab
PublisherSpringer Open
Pages203-213
Number of pages11
ISBN (Print)9783030396466
DOIs
Publication statusPublished - 2020
Event12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018 - London, United Kingdom
Duration: 9 Jul 201813 Jul 2018

Publication series

NameLecture Notes in Computational Science and Engineering
Volume134
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

Conference12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018
CountryUnited Kingdom
CityLondon
Period9/07/1813/07/18

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