应用数学和力学2024，Vol.45Issue(4)：490-501,12.DOI:10.21656/1000-0887.440293
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
摘要
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分类
力学引用本文复制引用
王媋瑗,李宏,何斯日古楞..非线性sine-Gordon方程的连续时空混合有限元方法[J].应用数学和力学,2024,45(4):490-501,12.基金项目
国家自然科学基金(12161063 （）
12161034) （）
内蒙古自然科学基金(2021MS01018) （2021MS01018）
内蒙古自治区高等学校创新团队发展计划(NMGIRT2207) （NMGIRT2207）
