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Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem

dc.contributor.authorAntonietti, Paola F.
dc.contributor.authorAyuso de Dios, Blanca
dc.contributor.authorMazzieri, Ilario
dc.contributor.authorQuarteroni, Alfio
dc.date.accessioned2017-05-15T10:35:10Z
dc.date.available2017-05-15T10:35:10Z
dc.date.issued2015-11-21
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.
dc.identifier.issn0885-7474
dc.identifier.issn1573-7691
dc.identifier.doi10.1007/s10915-015-0132-2
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.
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.
dc.publisherSpringer Nature
dc.subjectDiscontinuous Galerkin methods
dc.subjectElastodynamics equation
dc.subjectStability and error analysis
dc.titleStability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem
dc.typeArticle
dc.identifier.journalJournal of Scientific Computing
dc.contributor.institutionMOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
dc.contributor.institutionInstitut für Mathematik, Technische Universität Hamburg-Harburg, Hamburg, Germany
dc.contributor.institutionIstituto di Matematica Applicata e Tecnologie Informatiche (IMATI) – CNR, Pavia, Italy
dc.contributor.institutionDipartimento di Matematica, Università di Bologna, Bologna, Italy
dc.contributor.institutionCMCS, Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland
kaust.grant.numberBAS/1/1636−01−01
dc.date.published-online2015-11-21
dc.date.published-print2016-07


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