Anisotropic $EQ_1^{rot}$ 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 $EQ_1^{rot}$ 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 $EQ_1^{rot}$ 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.