A Superconvergent Nonconforming Mixed FEM for Multi-Term Time-Fractional Mixed Diffusion and Diffusion-Wave Equations with Variable Coefficients
Year: 2021
Author: Huijun Fan, Yanmin Zhao, Fenling Wang, Yanhua Shi, Yifa Tang
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 1 : pp. 63–92
Abstract
An unconditionally stable fully-discrete scheme on regular and anisotropic meshes for multi-term time-fractional mixed diffusion and diffusion-wave equations (TFMDDWEs) with variable coefficients is developed. The approach is based on a nonconforming mixed finite element method (FEM) in space and classical $L$1 time-stepping method combined with the Crank-Nicolson scheme in time. Then, the unconditionally stability analysis of the fully-discrete scheme is presented. The convergence for the original variable $u$ and the flux $\mathop{p} \limits ^{\rightarrow}=µ(\rm x)∇u$, respectively, in $H^1$- and $L^2$-norms is derived by using the relationship between the projection operator $R_h$ and the interpolation operator $I_h$. Interpolation postprocessing technique is used to establish superconvergence results. Finally, numerical tests are provided to demonstrate the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.180420.200720
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 1 : pp. 63–92
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Nonconforming mixed FEM multi-term time-fractional mixed diffusion and diffusion-wave equations $L$1 time-stepping method Crank-Nicolson scheme convergence and superconvergence.
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