Sine-Gordon方程的混合有限体积元方法及数值模拟

数学物理学报 ›› 2018, Vol. 38 ›› Issue (2): 395-416.

• 论文 • 上一篇

Sine-Gordon方程的混合有限体积元方法及数值模拟

方志朝¹, 李宏¹, 罗振东², 刘洋¹

1. 内蒙古大学数学科学学院呼和浩特 010021;
2. 华北电力大学数理学院北京 102206

收稿日期:2016-04-12 修回日期:2017-07-19 出版日期:2018-04-26 发布日期:2018-04-26
通讯作者: 李宏 E-mail:smslh@imu.edu.cn
作者简介:方志朝,E-mail:mazcfang@aliyun.com
基金资助:
国家自然科学基金（11701299，11761053，11661058，11671106），内蒙古自治区自然科学基金（2016-BS0105，2016MS0102，2017MS0107）和内蒙古自治区高等学校青年科技英才支持计划（NJYT-17-A07）

Mixed Finite Volume Element Method and Numerical Simulation for Sine-Gordon Equation

Fang Zhichao¹, Li Hong¹, Luo Zhendong², Liu Yang¹

1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021;
2. School of Mathematics and Physics, North China Electric Power University, Beijing 102206

Received:2016-04-12 Revised:2017-07-19 Online:2018-04-26 Published:2018-04-26
Supported by:
Supported by the NSFC (11701299, 11761053, 11661058, 11671106), the Natural Science Fund of Inner Mongolia Autonomous Region (2016BS0105, 2016MS0102, 2017MS0107) and Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (NJYT-17-A07)

摘要/Abstract

摘要： 研究了在Dirichlet边界条件和Neumann边界条件下一维sine-Gordon方程的混合有限体积元方法.通过引入将试探函数空间映射到检验函数空间的迁移算子γ_h，结合混合有限元方法和有限体积元方法，构造了半离散格式，时间显式和隐式全离散混合有限体积元格式.给出了显格式离散解的稳定性分析，并得到了三种格式的最优阶误差估计.最后，给出数值算例来验证理论分析结果和数值格式的有效性.

关键词: Sine-Gordon方程, 混合有限体积元方法, 最优误差估计

Abstract: The mixed finite volume element method for the one-dimensional sine-Gordon equation with Dirichlet or Neumann boundary conditions is developed and studied. By introducing a transfer operator γ_h which maps the trial function space into the test function space and combining mixed finite element with finite volume method, the continuous-in-time, explicit-in-time and implicit-in-time mixed finite volume element schemes are constructed. Stability analysis for explicit-in-time scheme is given, and optimal error estimates for three schemes are obtained. Finally, numerical experiments are given to verify the theoretical results and the effectiveness of the proposed schemes.

Key words: Sine-Gordon equation, Mixed finite volume element method, Optimal error estimate

中图分类号:

O242.21

方志朝, 李宏, 罗振东, 刘洋. Sine-Gordon方程的混合有限体积元方法及数值模拟[J]. 数学物理学报, 2018, 38(2): 395-416.

Fang Zhichao, Li Hong, Luo Zhendong, Liu Yang. Mixed Finite Volume Element Method and Numerical Simulation for Sine-Gordon Equation[J]. Acta mathematica scientia,Series A, 2018, 38(2): 395-416.

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Sine-Gordon方程的混合有限体积元方法及数值模拟

Mixed Finite Volume Element Method and Numerical Simulation for Sine-Gordon Equation

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