Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (6): 1599-1610.

• Articles • Previous Articles     Next Articles

High Accurary Analysis of the Bilinear Element for Nonlinear Dispersion-Dissipative Wave Equations

 WANG Fen-Ling1, SHI Dong-Yang2   

  1. 1.School of Mathematics and Statistics, Xuchang University, Henan Xuchang 461000;
    2.School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001
  • Received:2013-10-09 Revised:2014-11-08 Online:2014-12-25 Published:2014-12-25
  • Supported by:

    国家自然科学基金(10971203;11271340)、高等学校博士学科点专项科研基金(20094101110006)和河南省教育厅资助基金(14A110009)资助

Abstract:

The bilinear element approximation  is discussed  for a class of nonlinear dispersion-dissipative wave equations.
Based on the high acuraccy analysis of the element and interpolation post-processing technique, the optimal order error estimate, superclose property and superconvergence result in H1 norm are deduced for semi-discrete scheme under the proper regularity property hypothesis of the exact solution. At the same time, the extrapolation result with three order is
obtained by constructing a new extrapolation scheme. Finally, a fully-discrete scheme is established and the
superclose property is studied.

Key words: Nonlinear dispersion-dissipative wave equations, Superconvergence and extrapolation, Bilinear element,  
Semi-discrete and fully-discrete schemes

CLC Number: 

  • 65N15
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