Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1
Chinese Journal of Engineering Mathematics

Chinese Journal of Engineering Mathematics ›› 2015, Vol. 32 ›› Issue (1): 116-130.doi: 10.3969/j.issn.1005-3085.2015.01.012

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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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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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