非线性sine-Gordon方程的连续时空混合有限元方法
A Continuous Space-Time Mixed Finite Element Method for Sine-Gordon Equations
王媋瑗 1李宏 1何斯日古楞2
作者信息
- 1. 内蒙古大学 数学科学学院,呼和浩特 010021
- 2. 呼和浩特民族学院 数学科学学院,呼和浩特 010051
- 折叠
摘要
该文将混合有限元方法和连续时空有限元方法相结合,构造了sine-Gordon方程的连续时空混合有限元离散格式,引入独立变量p = ut来求解,并将时间变量和空间变量都用有限元方法处理.此格式可以将方程降阶,降低有限元空间的光滑性要求,同时在时间和空间两个方向都能发挥有限元方法的优势,获得时空高精度的数值解.理论分析中严格证明了数值解的稳定性,给出了u和p的误差估计.最后通过数值算例的结果展示了格式的有效性和可行性.
Abstract
The mixed finite element method was combined with the continuous space-time finite element meth-od to construct a continuous space-time mixed finite element scheme for sine-Gordon equations,through the introduction of independent variablep = utto solve the equations.This scheme uses the finite element method to treat both time and space variables.The space-time mixed finite element scheme can reduce the order of the e-quation and lower the smoothness requirements on the finite element space.The advantages of the finite ele-ment method was utilized in both the time and the space directions,thereby to obtain high-precision space-time numerical solutions.The stability of numerical solutions was strictly proven in the theoretical analysis,and er-ror estimates for u and p were provided.Finally,the effectiveness and feasibility of the proposed method were demonstrated through numerical examples.
关键词
sine-Gordon方程/连续时空混合有限元/稳定性/误差估计Key words
sine-Gordon equation/continuous space-time mixed finite element method/stability/error esti-mate引用本文复制引用
基金项目
国家自然科学基金(12161063)
国家自然科学基金(12161034)
内蒙古自治区自然科学基金(2021MS01018)
内蒙古自治区高等学校创新团队发展计划(NMGIRT2207)
出版年
2024
国家科技期刊平台
NSTL
万方数据