Issue |
ESAIM: M2AN
Volume 49, Number 4, July-August 2015
|
|
---|---|---|
Page(s) | 1085 - 1126 | |
DOI | https://doi.org/10.1051/m2an/2015001 | |
Published online | 30 June 2015 |
Analysis of a high-order space and time discontinuous Galerkin method for elastodynamic equations. Application to 3D wave propagation
1 Universitéde Lyon, CNRS UMR5208,
Université Lyon 1, Institut Camille Jordan, 43 blvd du 11 novembre 1918, 69622
Villeurbanne cedex,
France.
delcourte@math.univ-lyon1.fr
2 UCBL/INRIA Grenoble Rhône-Alpes/INSMI
− KALIFFE, France.
3 IFSTTAR/CEREMA, DTer
Méd., 56 boulevard
Stalingrad, 06359
Nice cedex 4,
France.
4 INRIA Sophia Antipolis Méditerranée,
team Nachos, 2004 route des
Lucioles, 06902
Sophia Antipolis cedex,
France.
Received:
11
July
2012
Revised:
17
October
2014
In this paper, we introduce a high-order discontinuous Galerkin method, based on centered fluxes and a family of high-order leap-frog time schemes, for the solution of the 3D elastodynamic equations written in velocity-stress formulation. We prove that this explicit scheme is stable under a CFL type condition obtained from a discrete energy which is preserved in domains with free surface or decreasing in domains with absorbing boundary conditions. Moreover, we study the convergence of the method for both the semi-discrete and the fully discrete schemes, and we illustrate the convergence results by the propagation of an eigenmode. We also propose a series of absorbing conditions which allow improving the convergence of the global scheme. Finally, several numerical applications of wave propagation, using a 3D solver, help illustrating the various properties of the method.
Mathematics Subject Classification: 35L50 / 35F10 / 35F15 / 35L05 / 35Q99
Key words: Discontinuous Galerkin method / centered flux / leap-frog scheme / elastodynamic equation
© EDP Sciences, SMAI 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.