Two new finite element schemes and their analysis for modeling of wave propagation in graphene
Two new finite element schemes and their analysis for modeling of wave propagation in graphene
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DOI：
10.1016/j.rinam.2020.100136
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发表时间：
2021-02
期刊：
影响因子：
--
通讯作者：
Jichun Li
中科院分区：
文献类型：
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作者：
Jichun Li
在本文中，我们研究了一个系统的控制方程模拟波在石墨烯中的传播。与我们以前的工作相比（Yang等人，2020），在这里，我们通过从原始模型中消除两个辅助未知量来重新研究控制方程。首次建立了该模型的一个全新的稳定性。自从Yang et al.（2020）在时间上仅为一阶，本文对简化的模拟方程提出了两种新的时间上二阶收敛的格式。离散稳定性继承完全相同的形式，连续稳定性证明了这两个计划。收敛误差估计也建立了两个计划。数值结果证明我们的理论分析。
In this paper, we investigate a system of governing equations for modeling wave propagation in graphene. Compared to our previous work (Yang et al., 2020) , here we re-investigate the governing equations by eliminating two auxiliary unknowns from the original model. A totally new stability for the model is established for the first time. Since the finite element scheme proposed in Yang et al. (2020) is only first order in time, here we propose two new schemes with second order convergence in time for the simplified modeling equations. Discrete stabilities inheriting exactly the same form as the continuous stability are proved for both schemes. Convergence error estimates are also established for both schemes. Numerical results are presented to justify our theoretical analysis.