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A Novel Discretization Method for Semilinear Reaction-Diffusion Equation

A Novel Discretization Method for Semilinear Reaction-Diffusion Equation

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 TH(Ω) (partition of domain Ω with mesh size H) with a large time step size Θ and a linearized equations on a fine mesh Th(Ω) (partition of domain Ω with mesh size h) using smaller time step size θ. Both theoretical and numerical results show that when h=H2,θ=Θ2, the novel two-grid numerical solution achieves the same approximate accuracy as that for the original semilinear problem directly by finite element method with Th(Ω) and θ.

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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.

Author Details

Luoping Chen

Yanping Chen

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