JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (10): 66-71.doi: 10.6040/j.issn.1671-9352.0.2014.128

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Superconvergence analysis and extrapolation of bilinear finite element for Schrödinger equation

WANG Ping-li1, 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:2014-03-31 Online:2014-10-20 Published:2014-11-10

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Abstract: The bilinear finite element approximation is mainly discussed for Schrödinger equation. The superclose property with O(h2)order is obtained in H1-norm by use of the derivative transfering skill and the high accuracy results of the element. Also, the global superconvergence result is given in H1-norm through the interpolation post-processing technique. Furthermore, through constructing a new extrapolation scheme, the extrapolation solution with O(h3)order is deduced which is two order higher than the traditional error estimate.

Key words: dinger equation, bilinear finite element, Schrö, superconvergence, extrapolation

CLC Number: 

  • O212.6
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