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A superconvergent hybridisable discontinuous Galerkin method for linear elasticity

Rubén Sevilla Orcid Logo, Matteo Giacomini, Alexandros Karkoulias, Antonio Huerta

International Journal for Numerical Methods in Engineering, Volume: 116, Issue: 2, Pages: 91 - 116

Swansea University Author: Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1002/nme.5916

Abstract

The first super‐convergent hybridisable discontinuous Galerkin (HDG) method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented. The key feature of the method is the strong imposition of the symmetry of the stress tensor...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 00295981
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa40780
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first_indexed 2018-06-21T13:26:51Z
last_indexed 2018-09-10T12:55:49Z
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spelling 2018-09-10T10:18:41.6263843 v2 40780 2018-06-21 A superconvergent hybridisable discontinuous Galerkin method for linear elasticity b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2018-06-21 CIVL The first super‐convergent hybridisable discontinuous Galerkin (HDG) method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented. The key feature of the method is the strong imposition of the symmetry of the stress tensor by means of the well‐known and extensively used Voigt notation, circumventing the use of complex mathematical concepts to enforce the symmetry of the stress tensor either weakly or strongly. A novel procedure to construct element‐by‐element a super‐convergent post‐processed displacement is proposed. Contrary to other HDG formulations, the methodology proposed here is able to produce a super‐convergent displacement field for low order approximations. The resulting method is robust and locking‐free in the nearly incompressible limit. An extensive set of numerical examples is utilised to provide evidence of the optimality of the method and its super‐convergent properties in two and three dimensions and for different element types. Journal Article International Journal for Numerical Methods in Engineering 116 2 91 116 00295981 Hybridisable discontinuous Galerkin, Elasticity, Mixed formulation, Voigt notation, Super‐convergence, Locking‐free 31 12 2018 2018-12-31 10.1002/nme.5916 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2018-09-10T10:18:41.6263843 2018-06-21T08:50:16.5995347 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Rubén Sevilla 0000-0002-0061-6214 1 Matteo Giacomini 2 Alexandros Karkoulias 3 Antonio Huerta 4 0040780-21062018085524.pdf sevilla2018(5).pdf 2018-06-21T08:55:24.3430000 Output 6720443 application/pdf Accepted Manuscript true 2019-06-27T00:00:00.0000000 true eng
title A superconvergent hybridisable discontinuous Galerkin method for linear elasticity
spellingShingle A superconvergent hybridisable discontinuous Galerkin method for linear elasticity
Rubén Sevilla
title_short A superconvergent hybridisable discontinuous Galerkin method for linear elasticity
title_full A superconvergent hybridisable discontinuous Galerkin method for linear elasticity
title_fullStr A superconvergent hybridisable discontinuous Galerkin method for linear elasticity
title_full_unstemmed A superconvergent hybridisable discontinuous Galerkin method for linear elasticity
title_sort A superconvergent hybridisable discontinuous Galerkin method for linear elasticity
author_id_str_mv b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author Rubén Sevilla
author2 Rubén Sevilla
Matteo Giacomini
Alexandros Karkoulias
Antonio Huerta
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 116
container_issue 2
container_start_page 91
publishDate 2018
institution Swansea University
issn 00295981
doi_str_mv 10.1002/nme.5916
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 1
active_str 0
description The first super‐convergent hybridisable discontinuous Galerkin (HDG) method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented. The key feature of the method is the strong imposition of the symmetry of the stress tensor by means of the well‐known and extensively used Voigt notation, circumventing the use of complex mathematical concepts to enforce the symmetry of the stress tensor either weakly or strongly. A novel procedure to construct element‐by‐element a super‐convergent post‐processed displacement is proposed. Contrary to other HDG formulations, the methodology proposed here is able to produce a super‐convergent displacement field for low order approximations. The resulting method is robust and locking‐free in the nearly incompressible limit. An extensive set of numerical examples is utilised to provide evidence of the optimality of the method and its super‐convergent properties in two and three dimensions and for different element types.
published_date 2018-12-31T03:51:55Z
_version_ 1763752558569979904
score 11.016235

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