arrow
Volume 15, Issue 2
Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative

Fangfang Cao, Yanmin Zhao, Fenling Wang, Yanhua Shi & Changhui Yao

Adv. Appl. Math. Mech., 15 (2023), pp. 322-358.

Published online: 2022-12

Export citation
  • Abstract

The main contents of this paper are to establish a finite element fully-discrete approximate scheme for multi-term time-fractional mixed sub-diffusion and diffusion-wave equation with spatial variable coefficient, which contains a time-space coupled derivative. The nonconforming $EQ_1^{rot}$ element and Raviart-Thomas element are employed for spatial discretization, and L1 time-stepping method combined with the Crank-Nicolson scheme are applied for temporal discretization. Firstly, based on some significant lemmas, the unconditional stability analysis of the fully-discrete scheme is acquired. With the assistance of the interpolation operator $I_h$ and projection operator $R_h$, superclose and convergence results of the variable $u$ in $H^1$-norm and the flux $\vec{p}=\kappa_5(\textbf{x})\nabla u(\textbf{x},t)$ in $L^2$-norm are obtained, respectively. Furthermore, the global superconvergence results are derived by applying the interpolation postprocessing technique. Finally, the availability and accuracy of the theoretical analysis are corroborated by experimental results of numerical examples on anisotropic meshes.

  • AMS Subject Headings

65M12, 65N30, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-15-322, author = {Cao , FangfangZhao , YanminWang , FenlingShi , Yanhua and Yao , Changhui}, title = {Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {15}, number = {2}, pages = {322--358}, abstract = {

The main contents of this paper are to establish a finite element fully-discrete approximate scheme for multi-term time-fractional mixed sub-diffusion and diffusion-wave equation with spatial variable coefficient, which contains a time-space coupled derivative. The nonconforming $EQ_1^{rot}$ element and Raviart-Thomas element are employed for spatial discretization, and L1 time-stepping method combined with the Crank-Nicolson scheme are applied for temporal discretization. Firstly, based on some significant lemmas, the unconditional stability analysis of the fully-discrete scheme is acquired. With the assistance of the interpolation operator $I_h$ and projection operator $R_h$, superclose and convergence results of the variable $u$ in $H^1$-norm and the flux $\vec{p}=\kappa_5(\textbf{x})\nabla u(\textbf{x},t)$ in $L^2$-norm are obtained, respectively. Furthermore, the global superconvergence results are derived by applying the interpolation postprocessing technique. Finally, the availability and accuracy of the theoretical analysis are corroborated by experimental results of numerical examples on anisotropic meshes.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0263}, url = {http://global-sci.org/intro/article_detail/aamm/21271.html} }
TY - JOUR T1 - Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative AU - Cao , Fangfang AU - Zhao , Yanmin AU - Wang , Fenling AU - Shi , Yanhua AU - Yao , Changhui JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 322 EP - 358 PY - 2022 DA - 2022/12 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2021-0263 UR - https://global-sci.org/intro/article_detail/aamm/21271.html KW - Multi-term time-fractional mixed sub-diffusion and diffusion-wave equation, nonconforming $EQ^{rot}_1$ mixed FEM, L1 approximation and Crank-Nicolson scheme, convergence and superconvergence. AB -

The main contents of this paper are to establish a finite element fully-discrete approximate scheme for multi-term time-fractional mixed sub-diffusion and diffusion-wave equation with spatial variable coefficient, which contains a time-space coupled derivative. The nonconforming $EQ_1^{rot}$ element and Raviart-Thomas element are employed for spatial discretization, and L1 time-stepping method combined with the Crank-Nicolson scheme are applied for temporal discretization. Firstly, based on some significant lemmas, the unconditional stability analysis of the fully-discrete scheme is acquired. With the assistance of the interpolation operator $I_h$ and projection operator $R_h$, superclose and convergence results of the variable $u$ in $H^1$-norm and the flux $\vec{p}=\kappa_5(\textbf{x})\nabla u(\textbf{x},t)$ in $L^2$-norm are obtained, respectively. Furthermore, the global superconvergence results are derived by applying the interpolation postprocessing technique. Finally, the availability and accuracy of the theoretical analysis are corroborated by experimental results of numerical examples on anisotropic meshes.

Fangfang Cao, Yanmin Zhao, Fenling Wang, Yanhua Shi & Changhui Yao. (2022). Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative. Advances in Applied Mathematics and Mechanics. 15 (2). 322-358. doi:10.4208/aamm.OA-2021-0263
Copy to clipboard
The citation has been copied to your clipboard