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Superconvergence analysis of a nonconforming finite element for #br# strongly damped wave equations

ZHANG Ya-dong1,  LI Xin-xiang2, SHI Dong-yang3   

  1. 1. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, Henan, China;
    2. College of Science, Shanghai University, Shanghai 200444, China;
    3.  School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, China
  • Received:2013-10-25 Online:2014-05-20 Published:2014-06-04

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Abstract: The superconvergence analysis of nonconforming finite element method for strongly damped wave equation is studied. The corresponding optimal order convergence error estimates and superclose property are obtained in broken H1-norm for both semi-discrete and fully-discrete schemes based on the interpolation of the element directly instead of the Ritz projection operator, which is an indispensabel tool in the traditional finite element analyis.The global superconvergence is derived through interpolation postprocessing technique. Finally, some numerical results are provided to show the validity of the theoretical analysis.

Key words: strongly damped wave equations, semidiscrete and fullydiscrete schemes, superclose, superconvergence, nonconforming finite element

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