报告主题：回火分数阶反应扩散方程的基于一样平常数值流通量的中止有限元要领

报告人：韦雷雷 副教授 （河南工业大学）

报告时间：2019年4月2日（周二）15：00

报告所在：校本部G507

约请人：李常品

主理部分：理学院数学系

报告摘要：The tempered fractional diffusion equation could be recognized as the generalization of the classic fractional diffusion equation that the truncation effects are included in the bounded domains. This paper focuses on designing the high order fully discrete local discontinuous Galerkin (LDG) method based on the generalized alternating numerical fluxes for the tempered fractional diffusion equation. From a practical point of view, the generalized alternating numerical flux which is different from the purely alternating numerical flux has a broader range of applications. We first design an efficient finite difference scheme to approximate the tempered fractional derivatives and then a fully discrete LDG method for the tempered fractional diffusion equation. We prove that the scheme is unconditionally stable and convergent with the order $O(h^{k+1}+\tau^{2-\alpha})$, where $h, \tau$ and $k$ are the step size in space, time and the degree of piecewise polynomials, respectively. Finally numerical experimets are performed to show the effectiveness and testify the accuracy of the method.

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