Stability of the high-order finite elements for acoustic or elastic wave propagation with high-order time stepping

Jonás D. De Basabe, Mrinal K. Sen

Research output: Contribution to journalArticlepeer-review

91 Scopus citations


We investigate the stability of some high-order finite element methods, namely the spectral element method and the interior-penalty discontinuous Galerkin method (IP-DGM), for acoustic or elastic wave propagation that have become increasingly popular in the recent past. We consider the Lax-Wendroff method (LWM) for time stepping and show that it allows for a larger time step than the classical leap-frog finite difference method, with higher-order accuracy. In particular the fourth-order LWM allows for a time step 73 per cent larger than that of the leap-frog method; the computational cost is approximately double per time step, but the larger time step partially compensates for this additional cost. Necessary, but not sufficient, stability conditions are given for the mentioned methods for orders up to 10 in space and time. The stability conditions for IP-DGM are approximately 20 and 60 per cent more restrictive than those for SEM in the acoustic and elastic cases, respectively. © 2010 The Authors Journal compilation © 2010 RAS.
Original languageEnglish (US)
Pages (from-to)577-590
Number of pages14
JournalGeophysical Journal International
Issue number1
StatePublished - Apr 2010
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: for their valuable feedback, and to Jean Virieux for his careful review. This work was partially supported by an AEA grant from the King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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