The discontinuous Galerkin finite element method for Caputo-type nonlinear conservation law
The discontinuous Galerkin finite element method for Caputo-type nonlinear conservation law
复制标题
Caputo型非线性守恒定律的间断伽辽金有限元法
DOI：
10.1016/j.matcom.2019.09.021
复制
发表时间：
2020-03-01
影响因子：
4.6
通讯作者：
Wang, Zhen
中科院分区：
文献类型：
--
作者：
Li, Changpin;Wang, Zhen
本文建立并研究了Caputo型非线性守恒律方程数值解的有效方法，其中时间分数阶导数采用有限差分法离散，空间分数阶导数采用间断Galerkin有限元法离散。推导出的数值格式的一个和两个空间维是稳定和收敛的。数值实验支持这些结论。(C)2019年国际数学与计算机模拟协会（IMACS）。由Elsevier B出版。版权所有© 2016
In this paper, efficient methods for numerical solutions of Caputo-type nonlinear conservation laws are established and studied, where the time fractional derivative with order in (0, 1) is discretized by the finite difference method and the spatial derivative by the discontinuous Galerkin finite element method. The derived numerical schemes for one and two space dimensions are shown to be stable and convergent. Numerical experiments are provided to support these conclusions. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B. V. All rights reserved.