TY - JOUR
T1 - Stability of the high-order finite elements for acoustic or elastic wave propagation with high-order time stepping
AU - De Basabe, Jonás D.
AU - Sen, Mrinal K.
N1 - 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.
PY - 2010/4
Y1 - 2010/4
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/599712
UR - https://academic.oup.com/gji/article-lookup/doi/10.1111/j.1365-246X.2010.04536.x
UR - http://www.scopus.com/inward/record.url?scp=77952577138&partnerID=8YFLogxK
U2 - 10.1111/j.1365-246X.2010.04536.x
DO - 10.1111/j.1365-246X.2010.04536.x
M3 - Article
SN - 0956-540X
VL - 181
SP - 577
EP - 590
JO - Geophysical Journal International
JF - Geophysical Journal International
IS - 1
ER -