摘要
本文得到了自然对流问题基于牛顿迭代两重网格算法的残量型后验误差估计.相对于标准有限元一层方法的后验误差估计,牛顿迭代两重网格算法的后验误差估计多了一些额外项.通过研究这些额外项的渐近行为,本文得到了这些额外项在误差估计中所起的作用.对于牛顿迭代两重网格方法的最优粗细网格匹配尺寸,这些额外项的收敛阶不高于离散解的收敛阶.数值算例验证了理论分析结论.
This paper presents the a posteriori error estimate of residual for natural convec-tion problem, which is computed by the two level Newton finite element method. The a posteriori error estimate contains additional terms in comparison to the one obtained by the standard one level finite element method. The action of the add-itional terms in the error estimate is investigated by studying their asymptotic behaviour. For optimally scaled meshes between coarse and fine meshes of the two level Newton finite element method, the additional terms are not of higher conver-gence order than the order of the numerical solution. Numerical experiments verify the obtained theory results.
出处
《工程数学学报》
CSCD
北大核心
2015年第1期116-130,共15页
Chinese Journal of Engineering Mathematics
基金
The National Natural Science Foundation of China(11171269
11401174)
the Ph.D.Programs Foundation of Ministry of Education of China(20110201110027)
the China Postdoctoral Science Foundation(2013M531311)
the Henan Scientific and Technological Research Project(132102310309)
the Educational Commission of Henan Province of China(14B110020
14B110021
14B110025)
the Doctoral Foundation of Henan University of Science and Technology(09001625)
the Science Foundation for Cultivating Innovation Ability of Henan University of Science and Technology(2014ZCX009)
the Youth Scientific Foundation of Henan University of Science and Technology(2012QN029)
关键词
两重网格有限元法
自然对流问题
后验误差估计
two level finite element method
natural convection problem
posteriori error estimate
