@Article{EAJAM-11-1,
author = {Huijun, Fan and Zhao, Yanmin and Wang, Fenling and Yanhua, Shi and Yifa, Tang},
title = {A Superconvergent Nonconforming Mixed FEM for Multi-Term Time-Fractional Mixed Diffusion and Diffusion-Wave Equations with Variable Coefficients},
journal = {East Asian Journal on Applied Mathematics},
year = {2021},
volume = {11},
number = {1},
pages = {63--92},
abstract = {<p style="text-align: justify;">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&nbsp;$\mathop{p} \limits ^{\rightarrow}=µ(\rm x)∇u$, 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.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.180420.200720},
url = {https://global-sci.com/article/82514/a-superconvergent-nonconforming-mixed-fem-for-multi-term-time-fractional-mixed-diffusion-and-diffusion-wave-equations-with-variable-coefficients}
}