数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1158-1169.

• 论文 • 上一篇    

抛物积分微分方程的Wilson元收敛性分析

梁聪刚1, 杨晓侠1, 石东洋2   

  1. 1 平顶山学院数学与统计学院 河南平顶山 467000;
    2 郑州大学数学与统计学院 郑州 450001
  • 收稿日期:2018-01-30 修回日期:2018-11-28 发布日期:2019-11-08
  • 作者简介:梁聪刚,E-mail:cgangl@126.com;杨晓侠,E-mail:13733937766@163.com;石东洋,E-mail:shi_dy@zzu.edu.cn
  • 基金资助:
    国家自然科学基金(11671369)、河南省科技计划项目(162300410082)和平顶山学院培育基金(PXY-PYJJ-2019006)

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)

摘要: 该文利用Wilson元对一类抛物积分微分方程提出了新的半离散和全离散逼近格式.基于单元的性质,通过定义新的双线性型,在不需要外推和插值后处理技术的前提下,分别得到了比传统的H1-范数更大的模意义下相应的Oh2)阶和Oh2+τ)阶的误差分析结果,比通常的关于Wilson元的误差估计高出一阶.这里,h,τ分别表示空间剖分参数和时间步长.最后,给出了一个数值算例,计算结果验证了理论分析的正确性.

关键词: 抛物积分微分方程, Wilson元, 半离散和全离散格式, 收敛性

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

中图分类号: 

  • O242.21