Year: 2018
Author: Luoping Chen, Yanping Chen
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 2 : pp. 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 $\mathcal{T}_H(\Omega)$ (partition of domain $\Omega$ with mesh size $H$) with a large time step size $\Theta$ and a linearized equations on a fine mesh $\mathcal{T}_h(\Omega)$ (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 semilinear problem directly by finite element method with $\mathcal{T}_h(\Omega)$ and $\theta$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2017-0011
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 2 : pp. 409–423
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Two-level discretization method semilinear reaction-diffusion equation convergence analysis.
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