自然对流问题两重网格算法的残量型后验误差估计(英文)  

Residual a Posteriori Error Estimate of Two Level Finite Element Method for Natural Convection Problem

作　　者：张运章[1,2] 侯延仁[3] 魏红波[3] 

机构地区：[1]河南科技大学数学与统计学院,洛阳471023 [2]南京大学数学系,南京210093 [3]西安交通大学数学与统计学院,西安710049

出　　处：《工程数学学报》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)

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.

关 键 词：两重网格有限元法 自然对流问题 后验误差估计 

分 类 号：O241[理学—计算数学]