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Crank-Nicolson Method of a Two-Grid Finite Volume Element Algorithm for Nonlinear Parabolic Equations

Crank-Nicolson Method of a Two-Grid Finite Volume Element Algorithm for Nonlinear Parabolic Equations
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Year:    2021

Author:    Yunjie Gong, Chuanjun Chen, Yuzhi Lou, Guanyu Xue

East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 3 : pp. 540–559

Abstract

A two-grid finite volume element algorithm based on Crank-Nicolson scheme for nonlinear parabolic equations is proposed. In this method, the nonlinear problem is solved on a coarse grid of size $H$ and a linear problem is considered on a fine grid of size $h$ by using the coarse-grid solution and one Newton iteration. This helps to improve the computing efficiency while keeping the accuracy. It is proved that the two-grid method can achieve asymptotically optimal error estimates in spaces and second order accuracy in time. Numerical results are consistent with the theoretical findings.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.090820.311220

East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 3 : pp. 540–559

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Crank-Nicolson method two-grid algorithm finite volume element method error estimates nonlinear parabolic equations.

Author Details

Yunjie Gong

Chuanjun Chen

Yuzhi Lou

Guanyu Xue

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