Efficient time discretization for local discontinuous Galerkin methods
Efficient time discretization for local discontinuous Galerkin methods
复制标题
局部间断伽辽金方法的高效时间离散
DOI：
10.3934/dcdsb.2007.8.677
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发表时间：
2007-07
影响因子：
1.2
通讯作者：
Xia, Yinhua
中科院分区：
文献类型：
--
作者：
Shu, Chi-Wang;Xu, Yan;Xia, Yinhua
In this paper, we explore three efficient time discretization techniques for the local discontinuous Galerkin (LDG) methods to solve partial differential equations (PDEs) with higher order spatial derivatives. The main difficulty is the stiffness of the LDG spatial discretization operator, which would require a unreasonably small time step for an explicit local time stepping method. We focus our discussion on the semi-implicit spectral deferred correction (SDC) method, and study its stability and accuracy when coupled with the LDG spatial discretization. We also discuss two other time discretization techniques, namely the additive Runge-Kutta (ARK) method and the exponential time differencing (ETD) method, coupled with the LDG spatial discretization. A comparison is made among these three time discretization techniques, to conclude that all three methods are efficient when coupled with the LDG spatial discretization for solving PDEs containing higher order spatial derivatives. In particular, the SDC method has the advantage of easy implementation for arbitrary order of accuracy, and the ARK method has the smallest CPU cost in our implementation.
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影响因子：
2.8
作者：
Kennedy, CA;Carpenter, MH
通讯作者：
Carpenter, MH
影响因子：
2
作者：
Bernardo Cockburn;S. Hou;Chi-Wang Shu
通讯作者：
Bernardo Cockburn;S. Hou;Chi-Wang Shu
影响因子：
2
作者：
Bernardo Cockburn;Chi-Wang Shu
通讯作者：
Bernardo Cockburn;Chi-Wang Shu
影响因子：
4.1
作者：
Bassi, F;Rebay, S
通讯作者：
Rebay, S
影响因子：
1
作者：
M. Minion
通讯作者：
M. Minion