运动方程一阶方程组格式的线性时域有限元及其EEP超收敛计算  

A LINEAR FINITE ELEMENT AND ITS EEP SUPER-CONVERGENT SOLUTION FOR FIRST ORDER ODES CONVERTED FROM MOTION EQUATIONS

作　　者：袁全 袁驷[1] YUAN Quan;YUAN Si(Department of Civil Engineering,Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry,Tsinghua University,Beijing 100084,China)

机构地区：[1]清华大学土木工程系,土木工程安全与耐久教育部重点实验室,北京100084

出　　处：《工程力学》2021年第S01期14-20,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(51878383,51378293)。

摘　　要：该文将运动方程转换成一阶常微分方程组,采用Galerkin线性单元,构建相应的h^(2)阶精度的递推公式,并基于单元能量投影(EEP)法进行结点位移修正得到h^(4)阶精度的有限元结点解。该文中对其稳定性和收敛阶给出数学分析和证明,同时给出了一个自适应步长算法,并通过数值算例验证其不失为一种有效、简洁的时域积分算法。The motion equation is transformed into a system of the first order differential equations(ODEs);and by using the linear finite element of the Galerkin type,the explicit recurrence formula is derived with an accuracy of O(h^(2)).By using the element energy projection(EEP)technique,the nodal accuracy recovery approach improves the recurrence formula to yield a nodal accuracy of O(h^(4)).Further,the stability property and convergence orders are analyzed mathematically with a given scheme of adaptive step-size.Finally,the given numerical examples justify that the proposed approach is a simple and effective method.

关 键 词：GALERKIN有限元法 运动方程 EEP超收敛 一阶方程组 结点位移精度修正 

分 类 号：O242.21[理学—计算数学]