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.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.Publisher
Springer NatureJournal
Journal of Scientific ComputingISSN
0885-74741573-7691
Handle URI
http://hdl.handle.net/10754/623596ae974a485f413a2113503eed53cd6c53
10.1007/s10915-015-0132-2