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Error Estimates of the Classical and Improved Two-Grid Methods

Error Estimates of the Classical and Improved Two-Grid Methods
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Year:    2018

Author:    Weifeng Zhang, Jinchao Xu, Liuqiang Zhong

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 4 : pp. 785–796

Abstract

In this paper, we obtain the first error estimate in $L^2$-norm for the classical two-grid method, then design an improved two-grid method by adding one more correction on the coarse space to the classical two-gird method. Furthermore, we also present the error estimates in both $L^2$-norm and $H^1$-norm for the improved two-grid method. Especially, the $L^2$ error estimate of the improved two-grid method is one order higher than that of the classical two-grid. At last, we confirm and illustrate the theoretical result by some numerical experiments.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2017-0212

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 4 : pp. 785–796

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Two-grid methods error estimate.

Author Details

Weifeng Zhang

Jinchao Xu

Liuqiang Zhong

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