Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (5): 1158-1169.

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Convergence Analysis of Wilson Element for Parabolic Integro-Differential Equation

Liang Conggang1, Yang Xiaoxia1, Shi Dongyang2   

  1. 1 School of Mathematics and Statistics, Pingdingshan University, Henan Pingdingshan 467000;
    2 School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001
  • Received:2018-01-30 Revised:2018-11-28 Published:2019-11-08
  • Supported by:
    Supported by the NSFC (11671369), the Science and Technology Planning Foundation of Henan Province (162300410082) and the University Cultivation Foundation of Pingdingshan (PXYPYJJ-2019006)

Abstract: In this paper, with the help of the wilson element, new semi-discrete and fullydiscrete schemes are proposed for parabolic integro-differential equation. Based on the properties of the element, through defining a new bilinear form, without using the technique of extrapolation and interpolated postprocessing, in the norm which is stronger than the usual H1-norm, the convergence results with order O(h2)/O(h2+τ) for the primitive solution are obtained for the corresponding schemes, respectively. The above results are just one order higher than the usual error estimates for the wilson element. Here, h and τ are parameters of the subdivision in space and time step, respectively. Finally, numerical results are provided to confirm the theoretical analysis.

Key words: Parabolic integro-differential equation, Wilson element, Semi-discrete and fulldiscrete schemes, Convergence

CLC Number: 

  • O242.21