JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (12): 35-46.doi: 10.6040/j.issn.1671-9352.0.2014.424

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Superconvergence and extrapolation of a lower order mixed finite method for nonlinear fourth-order hyperbolic equation

ZHANG Hou-chao, ZHU Wei-jun, WANG Jun-jun   

  1. School of Mathematics and Informatics, Pingdingshan University, Pingdingshan 467000, Henan, China
  • Received:2014-09-22 Revised:2015-03-06 Online:2015-12-20 Published:2015-12-23

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Abstract: With the help of the bilinear element Q11 and the Q01×Q10 element, a lower order conforming mixed finite element approximation scheme is proposed for nonlinear fourth-order hyperbolic equation. Firstly, the existence and uniqueness of approximation solution are proved. Secondly, Based on the known high accuracy results of the about two elements, by use of derivative delivery techniques, the superclose with order O(h2) for both scalar unknown u and the diffusion term v=-Δu in H1-norm and the flux p=-∇u in L2-norm are derived, respectively. Moreover, the global superconvergence is obtained through interpolation post-processing technique. Finally, throught constructing a new asymptotic expansion formula of Q01×Q10 element and a suitable extrapolation scheme, the extrapolation solutions with order O(h3) are derived. Here, h is the subdivision parameter for the space.

Key words: superclose, extrapolation, superconvergence, nonlinear fourth-order hyperbolic equation, mixed finite element methods

CLC Number: 

  • O242.21
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