@article{Zhao2025, 
author = {Jie Zhao and Zhichao Fang and Jiahuan Ren},
title = {A finite volume element method for the multi-term time fractional reaction-diffusion models with variable coefficients},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {20689-20714},
keywords = {finite volume element method, L1 formula, multi-term time fractional reaction-diffusion model, stability result, optimal error estimate},
url = {https://www.sciopen.com/article/10.3934/math.2025924},
doi = {10.3934/math.2025924},
abstract = {In this paper, a fully discrete finite volume element (FVE) scheme is proposed to treat the linear multi-term time fractional reaction-diffusion models with variable coefficients on triangular grids, where the Caputo fractional derivative of time variable is approximated by the    L  1 formula. The existence and uniqueness of solution for the proposed scheme is proved based on the matrix theories, the stability results are derived in detail by using a multi-term fractional Gronwall inequality, and the optimal error estimates under the        L    2    (  Ω  ) and        H    1    (  Ω  ) norms are also obtained. Owing to the variable coefficients in the models, a special technique should be used to analyze the stability and error estimates. Finally, three numerical examples with different fractional derivative terms are given to validate the feasibility and effectiveness.}
}