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Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations

Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations
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Year:    2021

Author:    Yuzhi Lou, Chuanjun Chen, Guanyu Xue

Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 4 : pp. 892–913

Abstract

The aim of the paper is to propose a second-order accurate Crank-Nicolson scheme for solving semilinear parabolic equations. This scheme combing two-grid finite volume element method involves solving a small nonlinear system on a coarse grid space and a linear system on a fine grid space, which can improve computing efficiency while keeping the accuracy. It means that we can use large time steps in the actual calculation. We further prove the optimal error estimates of the scheme strictly and present numerous simulations to demonstrate the theoretical results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2020-0064

Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 4 : pp. 892–913

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Two-grid method finite volume element method Crank-Nicolson scheme error estimates semilinear parabolic equations.

Author Details

Yuzhi Lou

Chuanjun Chen

Guanyu Xue

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