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

作　　者：王媋瑗 李宏 何斯日古楞 WANG Chunyuan;LI Hong;HE Siriguleng(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,P.R.China;School of Mathematical Sciences,Hohhot Minzu College,Hohhot 010051,P.R.China)

机构地区：[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

出　　处：《应用数学和力学》2024年第4期490-501,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12161063;12161034);内蒙古自然科学基金(2021MS01018);内蒙古自治区高等学校创新团队发展计划(NMGIRT2207)。

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=u_(t)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.The mixed finite element method was combined with the continuous space-time finite element method to construct a continuous space-time mixed finite element scheme for sine-Gordon equations,through the introduction of independent variable p=u_(t) to 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 equation and lower the smoothness requirements on the finite element space.The advantages of the finite element 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 error 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 

分 类 号：O357.41[理学—流体力学]