A new Hamilton principle of convolutional type, completely compatible with the initial conditions of an IVP, has been proposed in a recent publication arXiv:1912.08490v1 [math-ph]. In the present paper the possible use of this principle for the formulation of a FE scheme adjusted to dynamical problems is investigated. To this end, a FE scheme based on a convolutional extremum principle for the harmonic oscillator (used as an exemplary initial value problem) is developed and presented in detail. Besides, from the local finite element analysis a recurrent (one-step) algorithm arises which provides an approximate solution to the IVP, as well.T he succeeded schemes are computationally tested for both free and forced vibration problems.

翻译：在最近出版的一份出版物ArXiv:1912.08490v1 [math-ph]中提出了完全符合IVP初始条件的新的汉密尔顿卷发型新原则,在本文件中调查了是否可能使用这一原则来制定适应动态问题的FE计划,为此,为调和振动器开发并详细介绍了基于Colonic scremum 原则的FE计划(用作示范性的初步价值问题),此外,根据当地有限的要素分析,还产生了一种经常(一步)算法,为IVP提供了近似的解决办法。