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.