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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.
- Source :
-
Advances in Computational Mathematics . Jun2021, Vol. 47 Issue 3, p1-30. 30p. - Publication Year :
- 2021
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10197168
- Volume :
- 47
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Advances in Computational Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 150548054
- Full Text :
- https://doi.org/10.1007/s10444-021-09857-8