A finite element scheme for an initial value problem

2020/11/23 by Kalpakides, Vassilios K.
#49M99 #49S05 #70H25 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2011.11433

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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