Stability of the high-order finite elements for acoustic or elastic wave propagation with high-order time stepping
Stability of the high-order finite elements for acoustic or elastic wave propagation with high-order time stepping
复制标题
DOI：
10.1111/j.1365-246x.2010.04536.x
复制
发表时间：
2010-04-01
影响因子：
2.8
通讯作者：
Sen, Mrinal K.
中科院分区：
文献类型：
--
作者：
De Basabe, Jonas D.;Sen, Mrinal K.
我们研究了一些高阶有限元方法的稳定性，即谱元方法和罚函数间断伽辽金方法（IP-DGM），在最近的过去已经变得越来越流行的声波或弹性波传播。我们认为，Lax-Wendroff方法（LWM）的时间步长，并表明，它允许一个更大的时间步长比经典的蛙跳有限差分法，高阶精度。特别是四阶LWM允许的时间步长比蛙跳法大73%;计算成本大约是每个时间步长的两倍，但是较大的时间步长部分地补偿了这种额外的成本。必要的，但不是充分的，稳定性条件给出了所提到的方法的订单高达10在空间和时间。IP-DGM的稳定性条件是大约20%和60%以上的限制比那些SEM在声学和弹性的情况下，分别。
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.