当前位置: X-MOL 学术Math. Methods Appl. Sci. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
An SDG Galerkin structure‐preserving scheme for the Klein‐Gordon‐Schrödinger equation
Mathematical Methods in the Applied Sciences ( IF 2.9 ) Pub Date : 2020-03-25 , DOI: 10.1002/mma.6342
Jialing Wang 1, 2 , Yushun Wang 2
Affiliation  

In this paper, we use the Galerkin weak form to construct a structure‐preserving scheme for Klein‐Gordon‐Schrödinger equation and analyze its conservative and convergent properties. We first discretize the underlying equation in space direction via a selected finite element method, and the Hamiltonian partial differential equation can be casted into Hamiltonian ordinary differential equations based on the weak form of the system afterwards. Then, the resulted ordinary differential equations are solved by the symmetric discrete gradient method, which yields a charge‐preserving and energy‐preserving scheme. Moreover, the numerical solution of the proposed scheme is proved to be bounded in the discrete L norm and convergent with the convergence order of O ( h 2 + τ 2 ) in the discrete L 2 norm without any grid ratio restrictions, where h and τ are space and time step, respectively. Numerical experiments conducted last to verify the theoretical analysis.

中文翻译:

Klein-Gordon-Schrödinger方程的SDG Galerkin保留结构方案

在本文中,我们使用Galerkin弱形式为Klein-Gordon-Schrödinger方程构造一个保结构方案,并分析其保守和收敛性质。我们首先通过选择的有限元方法在空间方向上离散基础方程,然后根据系统的弱形式将哈密顿偏微分方程转换为哈密顿常微分方程。然后,通过对称离散梯度法求解所得的常微分方程,得到了一种电荷守恒和能量守恒的方案。此外,该方案的数值解被证明是有界的。 大号 规范与收敛顺序 Ø H 2 + τ 2 在离散 大号 2 没有任何网格比率限制的规范,其中 H τ 分别是空间和时间步长。最后进行的数值实验验证了理论分析。
更新日期:2020-03-25
down
wechat
bug