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arXiv · 2011.11433

A finite element scheme for an initial value problem

Vassilios K. Kalpakides
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Abstract

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.

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Vassilios K. Kalpakides. 2020-11-23. A finite element scheme for an initial value problem. https://arxiv.org/abs/2011.11433

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