East Asian J. Appl. Math., 11 (2021), pp. 63-92.
Published online: 2020-11
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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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.180420.200720}, url = {http://global-sci.org/intro/article_detail/eajam/18413.html} }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.