Anisotropic Finite Element Approximation for a Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation
Year: 2023
Author: Huijun Fan, Yanmin Zhao, Fenling Wang, Yanhua Shi, Fawang Liu
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 3 : pp. 458–481
Abstract
By employing nonconforming finite element, the numerical approximation is presented for multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on anisotropic meshes. Comparing with the multi-term time-fractional sub-diffusion equation or diffusion-wave equation, the mixed case contains a special time-space coupled derivative, which leads to many difficulties in numerical analysis. Firstly, a fully discrete scheme is established by using nonconforming finite element method (FEM) in spatial direction and L1 approximation coupled with Crank-Nicolson (L1-CN) scheme in temporal direction. Furthermore, the fully discrete scheme is proved to be unconditional stable. Besides, convergence and superclose results are derived by using the properties of nonconforming finite element. What's more, the global superconvergence is obtained via the interpolation postprocessing technique. Finally, several numerical results are provided to demonstrate the theoretical analysis on anisotropic meshes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2110-m2021-0180
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 3 : pp. 458–481
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Multi-term time-fractional mixed sub-diffusion and diffusion-wave equation Nonconforming FEM L1-CN scheme Anisotropic meshes Convergence and superconvergence.
Author Details
Huijun Fan Email
Yanmin Zhao Email
Fenling Wang Email
Yanhua Shi Email
Fawang Liu Email