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arXiv · 2309.02988

Fast time-stepping discontinuous Galerkin method for the subdiffusion equation

Hui Zhang·Fanhai Zeng·Xiaoyun Jiang·Zhimin Zhang
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Abstract

The nonlocality of the fractional operator causes numerical difficulties for long time computation of the time-fractional evolution equations. This paper develops a high-order fast time-stepping discontinuous Galerkin finite element method for the time-fractional diffusion equations, which saves storage and computational time. The optimal error estimate $O(N^{-p-1} + h^{m+1} + \varepsilon N^{rα})$ of the current time-stepping discontinuous Galerkin method is rigorous proved, where $N$ denotes the number of time intervals, $p$ is the degree of polynomial approximation on each time subinterval, $h$ is the maximum space step, $r\ge1$, $m$ is the order of finite element space, and $\varepsilon>0$ can be arbitrarily small. Numerical simulations verify the theoretical analysis.

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Hui Zhang, Fanhai Zeng, Xiaoyun Jiang, Zhimin Zhang. 2023-09-06. Fast time-stepping discontinuous Galerkin method for the subdiffusion equation. https://arxiv.org/abs/2309.02988

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