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 | |
| State | Published - Nov 21 2015 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged 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.