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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (1): 116-130.doi: 10.3969/j.issn.1005-3085.2015.01.012

• • 上一篇    下一篇

自然对流问题两重网格算法的残量型后验误差估计(英)

张运章1,2,    侯延仁3,   魏红波3   

  1. 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
  • 收稿日期:2013-10-08 接受日期:2014-04-24 出版日期:2015-02-15 发布日期:2015-04-15
  • 基金资助:
    国家自然科学基金 (11171269; 11401174)；教育部博士点基金 (20110201110027)；中国博士后科学基金 (2013M531311)；河南省科技攻关项目 (132102310309)；河南省教委 (14B110020; 14 b110021; 14 b110025)；河南科技大学博士基金 (09001625)；河南科技大学创新能力培养科学基金 (2014ZCX009)；河南科技大学青年科学基金 (2012QN029).

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

ZHANG Yun-zhang1,2,   HOU Yan-ren3,   WEI Hong-bo3   

  1. 1- School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023
    2- Department of Mathematics, Nanjing University, Nanjing 210093
    3- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
  • Received:2013-10-08 Accepted:2014-04-24 Online:2015-02-15 Published:2015-04-15
  • Supported by:
    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). 

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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．

关键词: 两重网格有限元法, 自然对流问题, 后验误差估计

Abstract:

This paper presents the a posteriori error estimate of residual for natural convection 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 convergence order than the order of the numerical solution. Numerical experiments verify the obtained theory results.

Key words: two level finite element method, natural convection problem, posteriori error estimate

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