Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem

Handle URI:
http://hdl.handle.net/10754/623596
Title:
Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem
Authors:
Antonietti, Paola F.; Ayuso de Dios, Blanca; Mazzieri, Ilario; Quarteroni, Alfio
Abstract:
We consider semi-discrete discontinuous Galerkin approximations of both displacement and displacement-stress formulations of the elastodynamics problem. We prove the stability analysis in the natural energy norm and derive optimal a-priori error estimates. For the displacement-stress formulation, schemes preserving the total energy of the system are introduced and discussed. We verify our theoretical estimates on two and three dimensions test problems.
Citation:
Antonietti PF, Ayuso de Dios B, Mazzieri I, Quarteroni A (2015) Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem. Journal of Scientific Computing 68: 143–170. Available: http://dx.doi.org/10.1007/s10915-015-0132-2.
Publisher:
Springer Nature
Journal:
Journal of Scientific Computing
KAUST Grant Number:
BAS/1/1636−01−01
Issue Date:
21-Nov-2015
DOI:
10.1007/s10915-015-0132-2
Type:
Article
ISSN:
0885-7474; 1573-7691
Sponsors:
Part of this work was carried out during several visits of the second author to the IMATI-CNR of Pavia. She is grateful to the IMATI for the kind hospitality and support. The work of the second author was partially supported by KAUST Grants BAS/1/1636−01−01 and Pocket ID 1000000193. The first and the third author have been partially supported by the INdAM-GNCS project “Nonstandard numerical methods for geophysics”. The first author has been also partially supported by the Italian research grant no. 2015-0182 “PolyNum: Metodi numerici poliedrici per equazioni alle derivate parziali” funded by Fondazione Cariplo and Regione Lombardia.
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Full metadata record

DC FieldValue Language
dc.contributor.authorAntonietti, Paola F.en
dc.contributor.authorAyuso de Dios, Blancaen
dc.contributor.authorMazzieri, Ilarioen
dc.contributor.authorQuarteroni, Alfioen
dc.date.accessioned2017-05-15T10:35:10Z-
dc.date.available2017-05-15T10:35:10Z-
dc.date.issued2015-11-21en
dc.identifier.citationAntonietti PF, Ayuso de Dios B, Mazzieri I, Quarteroni A (2015) Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem. Journal of Scientific Computing 68: 143–170. Available: http://dx.doi.org/10.1007/s10915-015-0132-2.en
dc.identifier.issn0885-7474en
dc.identifier.issn1573-7691en
dc.identifier.doi10.1007/s10915-015-0132-2en
dc.identifier.urihttp://hdl.handle.net/10754/623596-
dc.description.abstractWe consider semi-discrete discontinuous Galerkin approximations of both displacement and displacement-stress formulations of the elastodynamics problem. We prove the stability analysis in the natural energy norm and derive optimal a-priori error estimates. For the displacement-stress formulation, schemes preserving the total energy of the system are introduced and discussed. We verify our theoretical estimates on two and three dimensions test problems.en
dc.description.sponsorshipPart of this work was carried out during several visits of the second author to the IMATI-CNR of Pavia. She is grateful to the IMATI for the kind hospitality and support. The work of the second author was partially supported by KAUST Grants BAS/1/1636−01−01 and Pocket ID 1000000193. The first and the third author have been partially supported by the INdAM-GNCS project “Nonstandard numerical methods for geophysics”. The first author has been also partially supported by the Italian research grant no. 2015-0182 “PolyNum: Metodi numerici poliedrici per equazioni alle derivate parziali” funded by Fondazione Cariplo and Regione Lombardia.en
dc.publisherSpringer Natureen
dc.subjectDiscontinuous Galerkin methodsen
dc.subjectElastodynamics equationen
dc.subjectStability and error analysisen
dc.titleStability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problemen
dc.typeArticleen
dc.identifier.journalJournal of Scientific Computingen
dc.contributor.institutionMOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italyen
dc.contributor.institutionInstitut für Mathematik, Technische Universität Hamburg-Harburg, Hamburg, Germanyen
dc.contributor.institutionIstituto di Matematica Applicata e Tecnologie Informatiche (IMATI) – CNR, Pavia, Italyen
dc.contributor.institutionDipartimento di Matematica, Università di Bologna, Bologna, Italyen
dc.contributor.institutionCMCS, Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerlanden
kaust.grant.numberBAS/1/1636−01−01en
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