JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (08): 78-89.doi: 10.6040/j.issn.1671-9352.0.2014.410

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High accuracy analysis of the lowest order new mixed finite element scheme for generalized nerve conductive equations

FAN Ming-zhi1, WANG Fen-ling1, SHI Dong-yang2   

  1. 1. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, Henan, China;
    2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, China
  • Received:2014-09-16 Online:2015-08-20 Published:2015-07-31

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Abstract: A lowest order new mixed element approximate scheme with the bilinear element and Nédélec?s element for the generalized nerve conductive equations is proposed, which can satisfy Brezzi-Babuška condition automatically. Based on high accuracy analysis of the mixed element and interpolation post-processing technique, the superclose properties and superconvergence results of original variable in H1-norm and intermediate variable in L2-norm are deduced separately for semi-discrete scheme. At the same time, a second order fully-discrete scheme when is f(u) equal to f(X) is established and the superclose properties and the optimal order error estimates of original variable in H1-norm and intermediate variable in L2-norm are separately derived.

Key words: superclose properties and superconvergence results, new mixed element, the generalized nerve conductive equations, semi-discrete and fully-discrete schemes

CLC Number: 

  • O242.21
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