论文标题
初始值问题的有限元方案
A finite element scheme for an initial value problem
论文作者
论文摘要
在最近的出版物ARXIV：1912.08490V1 [Math-ph]中提出了一种与IVP初始条件完全兼容的新型汉密尔顿原则，与IVP的初始条件完全兼容。在本文中，研究了该原理可能使用该原理来调整为动态问题的FE方案的制定。为此，开发并详细介绍了基于谐波振荡器的卷积极值原理（用作示例性初始值问题）的FE方案。此外，从局部有限元分析中，出现了复发（一步）算法，该算法也为IVP提供了近似的解决方案。
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.
