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

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.