TY - JOUR
T1 - An Improved Two-Grid Technique for the Nonlinear Time-Fractional Parabolic Equation Based on the Block-Centered Finite Difference Method
AU - Li , Xiaoli
AU - Chen , Yanping
AU - Chen , Chuanjun
JO - Journal of Computational Mathematics
VL - 3
SP - 453
EP - 471
PY - 2022
DA - 2022/02
SN - 40
DO - http://doi.org/10.4208/jcm.2011-m2020-0124
UR - https://global-sci.org/intro/article_detail/jcm/20246.html
KW - Improved two-grid, Time-fractional parabolic equation, Nonlinear, Error estimates, Numerical experiments.
AB - <p style="text-align: justify;">A combined scheme of the improved two-grid technique with the block-centered finite difference method is constructed and analyzed to solve the nonlinear time-fractional parabolic equation. This method is considered where the nonlinear problem is solved only on a coarse grid of size $H$ and two linear problems based on the coarse-grid solutions and one Newton iteration is considered on a fine grid of size $h$. We provide the rigorous error estimate, which demonstrates that our scheme converges with order $\mathcal{O}(\Delta t^{2-\alpha}+h^2+H^4)$ on non-uniform rectangular grid. This result indicates that the improved two-grid method can obtain asymptotically optimal approximation as long as the mesh sizes satisfy $h=\mathcal{O}(H^2).$ Finally, numerical tests confirm the theoretical results of the presented method.</p>