Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem

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

Type

Article

Authors

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

KAUST Grant Number

BAS/1/1636−01−01

Date

2015-11-21

Online Publication Date

2015-11-21

Print Publication Date

2016-07

Permanent link to this record

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

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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.

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.