Discrete Maximum Principle and Energy Stability of the Compact Difference Scheme for Two-Dimensional Allen-Cahn Equation-Reference-Cited by-同舟云学术

Discrete Maximum Principle and Energy Stability of the Compact Difference Scheme for Two-Dimensional Allen-Cahn Equation

Published:2022-02-10 Issue: Volume:2022 Page:1-15
ISSN:2314-8888
Container-title:Journal of Function Spaces
language:en
Short-container-title:Journal of Function Spaces

Author:

Bo Yu¹,Tian Dan²,Liu Xiao¹^ORCID,Jin Yuanfeng¹^ORCID

Affiliation:

1. College of Science, Yanbian University, Yanji 133002, China

2. Public Course Department, Xi’an Traffic Engineering Institute, Xi’an 710000, China

Abstract

The Allen-Cahn model is discussed mainly in the phase field simulation. The compact difference method will be used to numerically approximate the two-dimensional nonlinear Allen-Cahn equation with initial and boundary value conditions, and then, a fully discrete compact difference scheme with second-order accuracy in time and fourth-order in space is established. And its numerical solution satisfies the discrete maximum principle under the constraints of reasonable space and time steps. On this basis, the energy stability of the scheme is investigated. Finally, numerical examples are given to illustrate the theoretical results.

Funder

Program for Young and Middle-Aged Leading Talents in Scientific and Technological Innovation of Jilin Province

Publisher

Hindawi Limited

Subject

Analysis

Link

http://downloads.hindawi.com/journals/jfs/2022/8522231.pdf

Reference12 articles.

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2. Discrete maximum principle and energy stability of finite difference methods for one-dimensional Allen-Cahn equations;J. Q. Zhang;Journal of Beihua University,2016

3. Numerical simulation of the three dimensional Allen–Cahn equation by the high-order compact ADI method

4. Comparison study of numerical methods for solving the Allen–Cahn equation

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