Virtual Element Method of the Allen-Cahn Equation

WANG Pei-zhen, TIAN Xu

doi:10.13371/j.cnki.chin.q.j.m.2023.01.002

Chinese Quarterly Journal of Mathematics >

2023 , Vol. 38 >Issue 1: 20 - 29

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2023.01.002

Virtual Element Method of the Allen-Cahn Equation

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School of Mathematics and Statistics, North China University of Water Resources and Electric Power,
Zhengzhou 450046, China

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

Received date: 2023-01-27

Online published: 2023-03-20

Supported by

Supported by National Natural Science Foundation of China (Grant No. 11901197); Young
Teacher Foundation of Henan Province (Grant No. 2021GGJS080).

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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

Cite this article

WANG Pei-zhen, TIAN Xu . Virtual Element Method of the Allen-Cahn Equation[J]. Chinese Quarterly Journal of Mathematics, 2023 , 38(1) : 20 -29 . DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.002

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