Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1880-1896.

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Discontinuous Galerkin Finite Element Analysis of for the Extended Fisher-Kolmogorov Equation

Xiaoxia Yang*(),Houchao Zhang   

  1. School of Mathematics and Statistics, Pingdingshan University, Henan Pingdingshan 467000
  • Received:2020-09-20 Online:2021-12-26 Published:2021-12-02
  • Contact: Xiaoxia Yang
  • Supported by:
    the NSFC(11271340);the NSFC(11671369);2020 Key Scientific Research Project of Henan Province Colleges and Universities(20A110030);2020 Key Scientific Research Project of Henan Province Colleges and Universities(20B110013);the Doctoral Starting Foundation of Pingdingshan University(PXY-BSQD-2019001)


The discontinuous Galerkin finite element approximation schemes for the Extended Fisher-Kolmogorov (EFK) equation are studied by using the Wilson element. Without using the technique of postprocessing technique, the convergence results with order $O(h^{2})/O(h^{2}+\tau)$ for the primitive solution $u$ and intermediate variable $v=-\triangle u$ are obtained for the semi-discrete and linearized Euler fully discrete approximation schemes respectively through a new splitting technique for the nonlinear terms. The above results are just one order higher than the usual error estimates of the Wilson element. Here, $h$ and $\tau$ are parameters of the subdivision in space and time step, respectively.

Key words: EFK equation, Discontinuous Galerkin finite element, Wilson element, Semi-discrete and fully-discrete schemes, Convergence

CLC Number: 

  • O242.21