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Volume 10, Issue 4
Error Estimates of the Classical and Improved Two-Grid Methods

Weifeng Zhang, Jinchao Xu & Liuqiang Zhong

Adv. Appl. Math. Mech., 10 (2018), pp. 785-796.

Published online: 2018-06

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  • 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.

  • Keywords

Two-grid methods, error estimate.

  • AMS Subject Headings

65N30, 65B99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-785, author = {Weifeng and Zhang and and 19127 and and Weifeng Zhang and Jinchao and Xu and and 19128 and and Jinchao Xu and Liuqiang and Zhong and and 19129 and and Liuqiang Zhong}, title = {Error Estimates of the Classical and Improved Two-Grid Methods}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0212}, url = {http://global-sci.org/intro/article_detail/aamm/12495.html} }
TY - JOUR T1 - Error Estimates of the Classical and Improved Two-Grid Methods AU - Zhang , Weifeng AU - Xu , Jinchao AU - Zhong , Liuqiang JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 785 EP - 796 PY - 2018 DA - 2018/06 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2017-0212 UR - https://global-sci.org/intro/article_detail/aamm/12495.html KW - Two-grid methods, error estimate. AB -

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.

Weifeng Zhang, Jinchao Xu & Liuqiang Zhong. (2020). Error Estimates of the Classical and Improved Two-Grid Methods. Advances in Applied Mathematics and Mechanics. 10 (4). 785-796. doi:10.4208/aamm.OA-2017-0212
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