JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (4): 90-98.doi: 10.6040/j.issn.1671-9352.0.2015.154

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New H 1-Galerkin mixed finite element analysis for quasi-linear viscoelasticity equation

DIAO Qun1, SHI Dong-yang2   

  1. 1. School of Mathematics and Information Science, Pingdingshan University, Pingdingshan 467000, Henan, China;
    2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, China
  • Received:2015-04-14 Online:2016-04-20 Published:2016-04-08

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Abstract: A new H 1-Galerkin mixed finite element pattern for quasi-linear viscoelasticity equation is constructed using incomplete biquadratic element Q-2 and first order BDFM element. Through Bramble-Hilbert lemma, a newhigh precision results of interpolation operators corresponding to unit are proved. Further, the superclose properties for the primitive variables u in H 1-norm and the intermediate variable (→overp) in H(div)-norm are obtained respectively in semi-discrete and fully discrete schemes.

Key words: quasi-linear viscoelasticity equation, H 1-Galerkin mixed finite element method, superclose, semi-discrete and fully discrete schemes, Bramble-Hilbert lemma

CLC Number: 

  • O242.21
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