@Article{AAMM-10-4,
author = {Zhang, Weifeng and Xu, Jinchao and Zhong, Liuqiang},
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 = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2017-0212},
url = {https://global-sci.com/article/73200/error-estimates-of-the-classical-and-improved-two-grid-methods}
}