数学季刊 ›› 2023, Vol. 38 ›› Issue (1): 20-29.doi: 10.13371/j.cnki.chin.q.j.m.2023.01.002

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Allen-Cahn方程的虚拟元方法

  

  1. School of Mathematics and Statistics, North China University of Water Resources and Electric Power,
    Zhengzhou 450046, China
  • 收稿日期:2023-01-27 出版日期:2023-03-30 发布日期:2023-03-20
  • 通讯作者: WANG Pei-zhen, (1982-), female, native of Nanyang, Henan, associate professor of North China University of Water Resources and Electric Power, engages in finite element method E-mail: peizhen86@126.com
  • 作者简介:WANG Pei-zhen, (1982-), female, native of Nanyang, Henan, associate professor of North China University of Water Resources and Electric Power, engages in finite element method; TIAN Xu (1997-), male, native of Xuchang, Henan, graduate student of North China University of Water Resources and Electric Power, engages in finite element method
  • 基金资助:
    Supported by National Natural Science Foundation of China (Grant No. 11901197); Young
    Teacher Foundation of Henan Province (Grant No. 2021GGJS080).

Virtual Element Method of the Allen-Cahn Equation

  1. School of Mathematics and Statistics, North China University of Water Resources and Electric Power,
    Zhengzhou 450046, China
  • Received:2023-01-27 Online:2023-03-30 Published:2023-03-20
  • Contact: WANG Pei-zhen, (1982-), female, native of Nanyang, Henan, associate professor of North China University of Water Resources and Electric Power, engages in finite element method E-mail: peizhen86@126.com
  • About author:WANG Pei-zhen, (1982-), female, native of Nanyang, Henan, associate professor of North China University of Water Resources and Electric Power, engages in finite element method; TIAN Xu (1997-), male, native of Xuchang, Henan, graduate student of North China University of Water Resources and Electric Power, engages in finite element method
  • Supported by:
    Supported by National Natural Science Foundation of China (Grant No. 11901197); Young
    Teacher Foundation of Henan Province (Grant No. 2021GGJS080).

PDF (PC)

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摘要：  In this article, the virtual element method of the Allen-Cahn equation on a
polygon grid is discussed in the fully discrete formulation. With the help of the energy
projection operator, we give the corresponding error estimates in the L2 norm and H1
norm.

关键词: The virtual element method, Allen-Cahn equation, Error estimation

Abstract:  In this article, the virtual element method of the Allen-Cahn equation on a
polygon grid is discussed in the fully discrete formulation. With the help of the energy
projection operator, we give the corresponding error estimates in the L2 norm and H1
norm.

Key words: The virtual element method, Allen-Cahn equation, Error estimation

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