@Article{JCM-41-3,
author = {Huijun, Fan and Zhao, Yanmin and Wang, Fenling and Yanhua, Shi and Liu, Fawang},
title = {Anisotropic $EQ_1^{rot}$ Finite Element Approximation for a Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation},
journal = {Journal of Computational Mathematics},
year = {2023},
volume = {41},
number = {3},
pages = {458--481},
abstract = {<p style="text-align: justify;">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&#39;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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2110-m2021-0180},
url = {https://global-sci.com/article/84125/anisotropic-eq-1rot-finite-element-approximation-for-a-multi-term-time-fractional-mixed-sub-diffusion-and-diffusion-wave-equation}
}