Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative
Year: 2023
Author: Fangfang Cao, Yanmin Zhao, Fenling Wang, Yanhua Shi, Changhui Yao
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 2 : pp. 322–358
Abstract
The main contents of this paper are to establish a finite element fully-discrete approximate scheme for multi-term time-fractional mixed sub-diffusion and diffusion-wave equation with spatial variable coefficient, which contains a time-space coupled derivative. The nonconforming $EQ_1^{rot}$ element and Raviart-Thomas element are employed for spatial discretization, and L1 time-stepping method combined with the Crank-Nicolson scheme are applied for temporal discretization. Firstly, based on some significant lemmas, the unconditional stability analysis of the fully-discrete scheme is acquired. With the assistance of the interpolation operator $I_h$ and projection operator $R_h$, superclose and convergence results of the variable $u$ in $H^1$-norm and the flux $\vec{p}=\kappa_5(\textbf{x})\nabla u(\textbf{x},t)$ in $L^2$-norm are obtained, respectively. Furthermore, the global superconvergence results are derived by applying the interpolation postprocessing technique. Finally, the availability and accuracy of the theoretical analysis are corroborated by experimental results of numerical examples on anisotropic meshes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0263
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 2 : pp. 322–358
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 37
Keywords: Multi-term time-fractional mixed sub-diffusion and diffusion-wave equation nonconforming $EQ^{rot}_1$ mixed FEM L1 approximation and Crank-Nicolson scheme convergence and superconvergence.
Author Details
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