TY - JOUR
T1 - Anisotropic $EQ_1^{rot}$ Finite Element Approximation for a Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation
AU - Fan , Huijun
AU - Zhao , Yanmin
AU - Wang , Fenling
AU - Shi , Yanhua
AU - Liu , Fawang
JO - Journal of Computational Mathematics
VL - 3
SP - 458
EP - 481
PY - 2023
DA - 2023/02
SN - 41
DO - http://doi.org/10.4208/jcm.2110-m2021-0180
UR - https://global-sci.org/intro/article_detail/jcm/21393.html
KW - Multi-term time-fractional mixed sub-diffusion and diffusion-wave equation, Nonconforming FEM, L1-CN scheme, Anisotropic meshes, Convergence and superconvergence.
AB - <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>