Adv. Appl. Math. Mech., 10 (2018), pp. 785-796.
Published online: 2018-06
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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} }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.