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Convergence of the space-time element method with rectangular elements

机译：时空元素方法与矩形元素的收敛性

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摘要

The convergence of the space-time element method (STEM) with linear, quadratic and cubic shape functions in time was studied. A standard procedure used for examining the convergence of multi-step methods for solving ordinary differential equations wa s applied. Diagrams of dispersion error and approximation errors of initial conditions and linear load changes are presented in the paper. It was Found that the STEM was free from errors connected with algorithmic dissipation. In order to verify the results of theoretical con- Siderations, the STEM was applied with a parabolic shape function to analyze the vibrations of a system with four degrees of freedom. The results obtained confirm the great precision of the STEM with non-linear shape functions.
机译：研究了具有线性，二次方和三次方函数的时空元素方法（STEM）在时间上的收敛性。应用了一种标准程序，该程序用于检查求解常微分方程的多步方法的收敛性。给出了初始条件和线性载荷变化的色散误差和近似误差图。发现STEM没有与算法耗散有关的错误。为了验证理论考虑的结果，STEM与抛物线形函数一起应用来分析具有四个自由度的系统的振动。获得的结果证实了具有非线性形状函数的STEM具有很高的精度。

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