@Article{AAMM-10-409,
author = {Luoping Chen and Yanping Chen},
title = {A Novel Discretization Method for Semilinear Reaction-Diffusion Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2018},
volume = {10},
number = {2},
pages = {409--423},
abstract = {In this work, we investigate a novel two-level discretization method for semilinear reaction-diffusion equations. Motivated by the two-grid method for nonlinear partial differential equations (PDEs) introduced by Xu [18] on physical space, our discretization method uses a two-grid finite element discretization method for semilinear partial differential equations on physical space and a two-level finite difference method for the corresponding time space. Specifically, we solve a semilinear equations on a coarse mesh $\mcal{T}_H(\Omega)$ (partition of domain $\Omega$ with mesh size $H$) with a large time step size $\Theta$ and a linearized equations on a fine mesh $\mcal{T}_h(\Omega)$ (partition of domain $\Omega$ with mesh size $h$) using smaller time step size $\theta$. Both theoretical and numerical results show that when $h=H^2, \theta=\Theta^2$, the novel two-grid numerical solution achieves the same approximate accuracy as that for the original seminlinear problem directly by finite element method with $\mcal{T}_h(\Omega)$ and $\theta$.},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2017-0011},
url = {http://global-sci.org/intro/article_detail/aamm/12218.html}
}