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05 May 2024

» arxiv » 2007.0420

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A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law
Yongseok Jang ; Simon Shaw ;
Date:	1 Jul 2020
Abstract:	We consider a fractional order viscoelasticity problem modelled by a power-law type stress relaxation function. This viscoelastic problem is a Volterra integral equation of the second kind with a weakly singular kernel where the convolution integral corresponds to fractional order differentiation/integration. We use a spatial finite element method and a finite difference scheme in time. Due to the weak singularity, fractional order integration in time is managed approximately by linear interpolation so that we can formulate a fully discrete problem. In this paper, we present a stability bound as well as a priori error estimates. Furthermore, we carry out numerical experiments with varying regularity of exact solutions at the end.
Source:	arXiv, 2007.0420
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