A tailored finite point method for subdiffusion equation with anisotropic and discontinuous diffusivity

• Published in: Applied mathematics and computation Vol. 401; p. 125907
• Main Authors: Wang, Yihong, Cao, Jianxiong
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.07.2021
• Subjects: Anisotropic; Discontinuous; Subdiffusion; Tailored finite point method; Anisotropic; Discontinuous; Tailored finite point method; Subdiffusion
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2020.125907

•This is the first attempt to construct tailored finite point method for subdiffusion equation with anisotropic and discontinuous diffusivity.•The most distinguished feature of this new scheme is that it not only can ensure high accuracy and stability for solving subdiffusion equations with high anisotropic diffusivity but also can efficiently resolve the high gradients near the side internal.•The unique solvability and unconditional stability of proposed scheme are strictly proved. In this paper, we first propose a tailored finite point method (TFPM) for solving time fractional subdiffusion problems with anisotropic and discontinuous diffusivity. This numerical scheme can perfectly capture the rapid transition of the solutions which contain sharp interface layers even with coarse meshes. Second, the accuracy and stability of the proposed scheme are strictly analyzed. Finally, some numerical examples are provided to show the accuracy and reliability of this new scheme.