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HDG-NEFEM with Degree Adaptivity for Stokes Flows

Rubén Sevilla Orcid Logo, Antonio Huerta

Journal of Scientific Computing, Volume: 77, Issue: 3, Pages: 1953 - 1980

Swansea University Author: Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1007/s10915-018-0657-2

Abstract

This paper presents the first degree adaptive procedure able to directly use the geometry given by a CAD model. The technique uses a hybridisable discontinuous Galerkin discretisation combined with a NURBS-enhanced rationale, completely removing the uncertainty induced by a polynomial approximation...

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Published in: Journal of Scientific Computing
ISSN: 0885-7474 1573-7691
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa38254
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spelling 2021-01-14T13:03:37.9470499 v2 38254 2018-01-23 HDG-NEFEM with Degree Adaptivity for Stokes Flows b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2018-01-23 CIVL This paper presents the first degree adaptive procedure able to directly use the geometry given by a CAD model. The technique uses a hybridisable discontinuous Galerkin discretisation combined with a NURBS-enhanced rationale, completely removing the uncertainty induced by a polynomial approximation of curved boundaries that is common within an isoparametric approach. The technique is compared against two strategies to perform degree adaptivity currently in use. This paper demonstrates, for the first time, that the most extended technique for degree adaptivity can easily lead to a non-reliable error estimator if no communication with CAD software is introduced whereas if the communication with the CAD is done, it results in a substantial computing time. The proposed technique encapsulates the CAD model in the simulation and is able to produce reliable error estimators irrespectively of the initial mesh used to start the adaptive process. Several numerical examples confirm the findings and demonstrate the superiority of the proposed technique. The paper also proposes a novel idea to test the implementation of high-order solvers where different degrees of approximation are used in different elements. Journal Article Journal of Scientific Computing 77 3 1953 1980 0885-7474 1573-7691 Hybridisable discontinuous Galerkin, NURBS-enhanced finite element method, Degree adaptivity, Stokes 1 12 2018 2018-12-01 10.1007/s10915-018-0657-2 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2021-01-14T13:03:37.9470499 2018-01-23T11:35:55.2822955 Rubén Sevilla 0000-0002-0061-6214 1 Antonio Huerta 2 0038254-09022018151017.pdf sevilla2018(2).pdf 2018-02-09T15:10:17.8170000 Output 9279786 application/pdf Version of Record true Released under the terms of a Creative Commons Attribution License (CC-BY). true eng http://creativecommons.org/licenses/by/4.0/
title HDG-NEFEM with Degree Adaptivity for Stokes Flows
spellingShingle HDG-NEFEM with Degree Adaptivity for Stokes Flows
Rubén Sevilla
title_short HDG-NEFEM with Degree Adaptivity for Stokes Flows
title_full HDG-NEFEM with Degree Adaptivity for Stokes Flows
title_fullStr HDG-NEFEM with Degree Adaptivity for Stokes Flows
title_full_unstemmed HDG-NEFEM with Degree Adaptivity for Stokes Flows
title_sort HDG-NEFEM with Degree Adaptivity for Stokes Flows
author_id_str_mv b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author Rubén Sevilla
author2 Rubén Sevilla
Antonio Huerta
format Journal article
container_title Journal of Scientific Computing
container_volume 77
container_issue 3
container_start_page 1953
publishDate 2018
institution Swansea University
issn 0885-7474
1573-7691
doi_str_mv 10.1007/s10915-018-0657-2
document_store_str 1
active_str 0
description This paper presents the first degree adaptive procedure able to directly use the geometry given by a CAD model. The technique uses a hybridisable discontinuous Galerkin discretisation combined with a NURBS-enhanced rationale, completely removing the uncertainty induced by a polynomial approximation of curved boundaries that is common within an isoparametric approach. The technique is compared against two strategies to perform degree adaptivity currently in use. This paper demonstrates, for the first time, that the most extended technique for degree adaptivity can easily lead to a non-reliable error estimator if no communication with CAD software is introduced whereas if the communication with the CAD is done, it results in a substantial computing time. The proposed technique encapsulates the CAD model in the simulation and is able to produce reliable error estimators irrespectively of the initial mesh used to start the adaptive process. Several numerical examples confirm the findings and demonstrate the superiority of the proposed technique. The paper also proposes a novel idea to test the implementation of high-order solvers where different degrees of approximation are used in different elements.
published_date 2018-12-01T03:51:59Z
_version_ 1737026458051674112
score 10.899931

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