数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1880-1896.

• 论文 • 上一篇    下一篇

Extended Fisher-Kolmogorov方程的间断有限元分析

杨晓侠*(),张厚超   

  1. 平顶山学院数学与统计学院 河南平顶山 467000
  • 收稿日期:2020-09-20 出版日期:2021-12-26 发布日期:2021-12-02
  • 通讯作者: 杨晓侠 E-mail:yangxiaoxia1014@163.com
  • 基金资助:
    国家自然科学基金(11271340);国家自然科学基金(11671369);2020年度河南省高等学校重点科研项目(20A110030);2020年度河南省高等学校重点科研项目(20B110013);平顶山学院高层次人才启动基金(PXY-BSQD-2019001)

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 E-mail:yangxiaoxia1014@163.com
  • 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)

摘要:

利用Wilson元研究了Extended Fisher-Kolmogorov(EFK)方程的间断有限元逼近格式.在不需要后处理技术的前提下,通过对非线性项采用新的分裂技术,分别得到了半离散和线性化欧拉全离散格式下原始变量$u$和中间变量$v=-\triangle u$$O(h^{2})$$O(h^{2}+\tau)$阶的收敛性结果,正好比通常的关于Wilson元的误差估计高出一阶.这里,$h$$\tau$表示空间剖分参数和时间步长.

关键词: EFK方程, 间断有限元, Wilson元, 半离散和全离散格式, 收敛性

Abstract:

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

中图分类号: 

  • O242.21