Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (4): 894-908.

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Superconvergence Analysis of an H1-Galerkin Mixed Finite Element Method for Nonlinear Parabolic Equation

Junjun Wang*(),Xiaoxia Yang   

  1. School of Mathematics and Statistics, Pingdingshan University, Henan Pingdingshan 467000
  • Received:2018-02-28 Online:2019-08-26 Published:2019-09-11
  • Contact: Junjun Wang
  • Supported by:
    国家自然科学基金(11671369);平顶山学院博士启动基金(PXY-BSQD-2019001);平顶山学院培育基金(PXY-PYJJ-2019006);the NSFC(11671369);the Doctoral Starting Foundation of PingdingshanUniversity(PXY-BSQD-2019001);the University Cultivation Foundation of Pingdingshan(PXY-PYJJ-2019006)


Nonlinear parabolic equation is studied by H1-Galerkin mixed finite element method. The bilinear element and the zero-order Raviart-Thomas elements are utilized to discuss superclose properties of the original variable u in H1(Ω) and the flux p=▽u in H(div; Ω) under the semi-discrete scheme and Euler fully-discrete scheme. During the process, the splitting technique is used and the regularity of u and p are not improved. The numerical example confirm the theory.

Key words: Nonlinear parabolic equation, H1-Galerkin mixed finite element method, The semi-discrete scheme and Euler fully-discrete scheme, Superclose properties

CLC Number: 

  • O242.21