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 journalArticlepeer-review

29 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 languageEnglish (US)
Pages (from-to)143-170
Number of pages28
JournalJournal of Scientific Computing
Volume68
Issue number1
DOIs
StatePublished - Nov 21 2015
Externally publishedYes

Bibliographical 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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