论文标题
动态粘弹性问题的有限元近似的先验误差分析，涉及分数阶数差异性本构定律
A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law
论文作者
论文摘要
我们考虑由幂律类型应力松弛函数建模的分数粘弹性问题。这个粘弹性问题是第二种的Volterra积分方程，具有弱奇异的内核，其中卷积积分对应于分数阶的分化/整合。我们使用空间有限元方法和时间的有限差方案。由于奇异性较弱，时间插值大致管理分数阶的积分，以便我们可以制定一个完全离散的问题。在本文中，我们提出稳定性结合以及先验误差估计。此外，我们进行数值实验，最终具有不同的精确溶液的规律性。
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.
