ABSTRACT

In this paper, we consider the numerical approximation of the modified anomalous subdiffusion model which involves the Riemann–Liouville derivatives in time. We propose two robust fully discrete finite element methods by employing the piecewise linear Galerkin finite element method in space and the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods. The error estimates for semidiscrete and fully discrete schemes are investigated with respect to the data regularity. Furthermore, we numerically compare our numerical schemes with a Crank–Nicolson finite element method to illustrate the efficiency of our methods and confirm the theoretical results.

摘要

在本文中，我们考虑了修正的异常子扩散模型的数值近似，该模型涉及时间上的 Riemann-Liouville 导数。我们通过在空间上采用分段线性伽辽金有限元方法和由后向欧拉和二阶后向差分方法生成的时间上的卷积正交，提出了两种鲁棒的全离散有限元方法。半离散和完全离散方案的误差估计就数据的规律性进行了研究。此外，我们将我们的数值方案与 Crank-Nicolson 有限元方法进行数值比较，以说明我们方法的效率并确认理论结果。