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 (6): 927-940.doi: 10.3969/j.issn.1005-3085.2015.06.014

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Adaptive Defect Correction for Linearized Viscoelastic Flow

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

  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:2013-09-17 Accepted:2014-12-02 Online:2015-12-15 Published:2016-02-15
  • Supported by:
    The National Natural Science Foundation of China (11171269;  11401074);  the Ph.D. Program Foundation of Ministry of Education of China (20110201110027);  the China Postdoctoral Science Foundation (2013M531311);  the Research Fund of Educational Commission of Henan Province of China (14B110020;  14B110021;  14B110025);  the Henan Scientific and Technological Research Project (132102310309);  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 is concerned with some numerical computation on viscoelastic non-Newtonian fluids. Viscoelastic non-Newtonian fluids can be viewed as the intermediate states between the fluids and the solids. As viscoelastic non-Newtonian fluids is complex, it is very difficult to numerically solve the problem. In this paper, we combine the defect correction method and the adaptive method to study linearized viscoelastic fluid flow. A reliable a posteriori error estimate is derived for the adaptive defect correction method. Numerical experiments are provided which ill-ustrate the utility of the resulting adaptive defect correction method for linearized viscoelastic fluid flow. The obtained results can be viewed as the basis for further research on more complex viscoelastic non-Newtonian fluids.

Key words: linearized viscoelastic fluid flow, finite element method, adaptive defect correction method, posteriori error estimate

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