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DC Field | Value | Language |
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dc.contributor.author | Jang, Y | - |
dc.contributor.author | Shaw, S | - |
dc.date.accessioned | 2023-02-22T12:51:44Z | - |
dc.date.available | 2023-02-22T12:51:44Z | - |
dc.date.issued | 2023-02-22 | - |
dc.identifier | ORCID iD: Yongseok Jang https://orcid.org/0000-0002-2036-558X | - |
dc.identifier | ORCID iD: Simon Shaw https://orcid.org/0000-0003-1406-7225 | - |
dc.identifier.citation | Jang, Y. and Shaw, S. (2023) 'A Priori Analysis of a Symmetric Interior Penalty Discontinuous Galerkin Finite Element Method for a Dynamic Linear Viscoelasticity Model', Computational Methods in Applied Mathematics, 23 (3), pp. 1 - 21. doi: 10.1515/cmam-2022-0201. | en_US |
dc.identifier.issn | 1609-4840 | - |
dc.identifier.uri | https://bura.brunel.ac.uk/handle/2438/25989 | - |
dc.description.abstract | The stress-strain constitutive law for viscoelastic materials such as soft tissues, metals at high temperature, and polymers can be written as a Volterra integral equation of the second kind with a fading memory kernel. This integral relationship yields current stress for a given strain history and can be used in the momentum balance law to derive a mathematical model for the resulting deformation. We consider such a dynamic linear viscoelastic model problem resulting from using a Dirichlet–Prony series of decaying exponentials to provide the fading memory in the Volterra kernel. We introduce two types of internal variable to replace the Volterra integral with a system of auxiliary ordinary differential equations and then use a spatially discontinuous symmetric interior penalty Galerkin (SIPG) finite element method and – in time – a Crank–Nicolson method to formulate the fully discrete problems: one for each type of internal variable. We present a priori stability and error analyses without using Grönwall’s inequality and with the result that the constants in our estimates grow linearly with time rather than exponentially. In this sense, the schemes are therefore suited to simulating long time viscoelastic response, and this (to our knowledge) is the first time that such high quality estimates have been presented for SIPG finite element approximation of dynamic viscoelasticity problems. We also carry out a number of numerical experiments using the FEniCS environment (https://fenicsproject.org), describe a simulation using “real” material data, and explain how the codes can be obtained and all of the results reproduced. | en_US |
dc.description.sponsorship | Y. Jang acknowledges the support of a Brunel University London Doctoral scholarship. | en_US |
dc.format.extent | 1 - 23 | - |
dc.format.medium | Print-Electronic | - |
dc.language.iso | en_US | en_US |
dc.publisher | Walter de Gruyter | en_US |
dc.rights | Copyright © Walter de Gruyter GmbH 2023. All rights reserved. The final publication is available at https://www.degruyter.com/document/doi/10.1515/cmam-2022-0201/html. De Gruyter allows authors the use of the final published version of an article (publisher pdf) for self-archiving (author's personal website) and/or archiving in an institutional repository (on a non-profit server) after an embargo period of 12 months after publication. The published source must be acknowledged and a link to the journal home page or articles' DOI must be set. Authors MAY NOT self-archive their articles in public and/or commercial subject based repositories (see: https://www.degruyter.com/publishing/services/rights-and-permissions/repositorypolicy and https://degruyter-live-craftcms-assets.s3.amazonaws.com/docs/CopyrightTransferAgreementDeGruyter.pdf). | - |
dc.rights.uri | https://www.degruyter.com/publishing/services/rights-and-permissions/repositorypolicy | - |
dc.subject | viscoelasticity | en_US |
dc.subject | generalised Maxwell solid | en_US |
dc.subject | symmetric interior penalty | en_US |
dc.subject | discontinuous Galerkin finite element method | en_US |
dc.subject | a priori analysis | en_US |
dc.subject | internal variables | en_US |
dc.title | A Priori Analysis of a Symmetric Interior Penalty Discontinuous Galerkin Finite Element Method for a Dynamic Linear Viscoelasticity Model | en_US |
dc.type | Article | en_US |
dc.identifier.doi | https://doi.org/10.1515/cmam-2022-0201 | - |
dc.relation.isPartOf | Computational Methods in Applied Mathematics | - |
pubs.issue | 3 | - |
pubs.publication-status | Published | - |
pubs.volume | 23 | - |
dc.identifier.eissn | 1609-9389 | - |
dc.rights.holder | Walter de Gruyter | - |
Appears in Collections: | Dept of Mathematics Embargoed Research Papers |
Files in This Item:
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FullText.pdf | Embargoed until 22 February 2024 | 2.43 MB | Adobe PDF | View/Open |
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