TY - JOUR
T1 - Error estimates of the classical and improved two-gridmethods
AU - Zhang, Weifeng
AU - Xu, Jinchao
AU - Zhong, Liuqiang
N1 - Funding Information:
The work of the first author was supported in part by Yunnan Provincial Science and Technology Department Research Award: Interdisciplinary Research in Computational Mathematics and Mechanics with Applications in Energy Engineering (Grant
Funding Information:
No. 2009CI128). The work of the second author was supported in part by Yunnan Provincial Science and Technology Project (Grant No. 2014RA071). The work of the third author was supported in part by National Natural Science Foundation of China (Grant No. 11671159), Natural Science Foundation of Guangdong Province (Grant No. 2016A030313842) and the Characteristic Innovation Project from the Educational Department of Guangdong Province (Grant No. 2016KTSCX024).
Publisher Copyright:
© 2018 Global Science Press.
PY - 2018
Y1 - 2018
N2 - 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 L2 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.
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 L2 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.
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U2 - 10.4208/aamm.OA-2017-0212
DO - 10.4208/aamm.OA-2017-0212
M3 - Article
AN - SCOPUS:85069495964
SN - 2070-0733
VL - 10
SP - 785
EP - 796
JO - Advances in Applied Mathematics and Mechanics
JF - Advances in Applied Mathematics and Mechanics
IS - 4
ER -