Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem

Paola F. Antonietti; Blanca Ayuso de Dios; Ilario Mazzieri; Alfio Quarteroni

doi:10.1007/s10915-015-0132-2

Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem

Paola F. Antonietti, Blanca Ayuso de Dios, Ilario Mazzieri, Alfio Quarteroni

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

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.

Original language	English (US)
Pages (from-to)	143-170
Number of pages	28
Journal	Journal of Scientific Computing
Volume	68
Issue number	1
DOIs	https://doi.org/10.1007/s10915-015-0132-2
State	Published - Nov 21 2015
Externally published	Yes

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title = "Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem",

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.",

author = "Antonietti, {Paola F.} and {Ayuso de Dios}, Blanca and Ilario Mazzieri and Alfio Quarteroni",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): BAS/1/1636−01−01 Acknowledgements: 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. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1007/s10915-015-0132-2",

language = "English (US)",

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T1 - Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem

AU - Antonietti, Paola F.

AU - Ayuso de Dios, Blanca

AU - Mazzieri, Ilario

AU - Quarteroni, Alfio

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): BAS/1/1636−01−01 Acknowledgements: 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. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2015/11/21

Y1 - 2015/11/21

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/623596

UR - http://link.springer.com/10.1007/s10915-015-0132-2

UR - http://www.scopus.com/inward/record.url?scp=84947714299&partnerID=8YFLogxK

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DO - 10.1007/s10915-015-0132-2

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VL - 68

SP - 143

EP - 170

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 1

ER -

Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem

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