Space-time finite element method for the multi-term time-space fractional diffusion equation on a two-dimensional domain
Space-time finite element method for the multi-term time-space fractional diffusion equation on a two-dimensional domain
复制标题
二维域上多项时空分数扩散方程的时空有限元法
DOI：
10.1016/j.camwa.2018.11.033
复制
发表时间：
2019-09-01
影响因子：
2.9
通讯作者：
Zeng, Wei
中科院分区：
文献类型：
--
作者：
Bu, Weiping;Shu, Shi;Zeng, Wei
在本文中，我们提出了一种用于多项时空分数扩散方程的时空有限元方法。首先，列出了一些分数阶导数空间，给出了分数阶导数和分数阶导数空间的一些性质，介绍了有限元空间的一些定义和性质，并针对所考虑的问题提出了时空有限元全离散格式。其次，讨论了所得数值格式的存在性、唯一性和稳定性。第三，在 t = 0 附近精确解奇异行为的假设下，基于合适的分级时间网格详细研究了收敛性。最后通过数值试验验证了该方法的合理性和有效性。 (C) 2018 Elsevier Ltd. 保留所有权利。
In this paper, we propose a space-time finite element method for the multi-term time-space fractional diffusion equation. First, some fractional derivative spaces are listed, some properties of the fractional derivatives and fractional derivative spaces are given, some definitions and properties of finite element spaces are introduced, and a space-time finite element fully discrete scheme for the considered problem is developed. Second, the existence, uniqueness and stability of the obtained numerical scheme are discussed. Third, under the hypothesis about singular behavior of exact solution near t = 0, the convergence is investigated in detail based on the suitable graded time mesh. At last, some numerical tests are given to verify the rationality and effectiveness of our method. (C) 2018 Elsevier Ltd. All rights reserved.