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 L2-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 L2-norm and H1-norm for the improved two-grid method. Especially, the L2error 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 = {}, 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 L2-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 L2-norm and H1-norm for the improved two-grid method. Especially, the L2error 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 JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 785 EP - 796 PY - 2018 DA - 2018/06 SN - 10 DO - http://dor.org/10.4208/aamm.OA-2017-0212 UR - https://global-sci.org/intro/aamm/12495.html KW - Two-grid methods, error estimate. AB -

In this paper, we obtain the first error estimate in L2-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 L2-norm and H1-norm for the improved two-grid method. Especially, the L2error 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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