تقرير
A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law
| العنوان: | A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law |
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| المؤلفون: | Jang, Yongseok, Shaw, Simon |
| المصدر: | 46 (2021) |
| سنة النشر: | 2020 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 74D05, 74S05, 45D05 |
| الوصف: | 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. Comment: Accepted by Advances in Computational Mathematics |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s10444-021-09857-8 |
| URL الوصول: | http://arxiv.org/abs/2007.00420 |
| رقم الأكسشن: | edsarx.2007.00420 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s10444-021-09857-8 |
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