A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law
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.
Keywords
Cite
@article{arxiv.2007.00420,
title = {A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law},
author = {Yongseok Jang and Simon Shaw},
journal= {arXiv preprint arXiv:2007.00420},
year = {2021}
}
Comments
Accepted by Advances in Computational Mathematics