UNIFORM L-p-BOUND OF THE ALLEN-CAHN EQUATION AND ITS NUMERICAL DISCRETIZATION

Yang, Jiang1; Du, Qiang2; Zhang, Wei3,4

2018

International Journal of Numerical Analysis and Modeling   影响因子和分区

1705-5105

We study uniform bounds associated with the Allen-Cahn equation and its numerical discretization schemes. These uniform bounds are different from, and weaker than, the conventional energy dissipation and the maximum principle, but they can be helpful in the analysis of numerical methods. In particular, we show that finite difference spatial discretization, like the original continuum model, shares the uniform L-p-bound for all even p, which also leads to the maximum principle. In comparison, a couple of other spatial discretization schemes, namely the Fourier spectral Galerkin method and spectral collocation method preserve the L-p-bound only for p = 2. Moreover, fully discretized schemes based on the Fourier collocation method for spatial discretization and Strang splitting method for time discretization also preserve the uniform L-2-bound unconditionally.

Allen-Cahn Equations maximum principle operator splitting uniform L-p-bound Fourier spectral methods

SCI

英语

第一

[NSFC-91630207]

Mathematics

Mathematics, Applied ; Mathematics

WOS:000428719500012

ISCI-INST SCIENTIFIC COMPUTING & INFORMATION

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen, Guangdong, Peoples R China
2.Columbia Univ, Dept Appl Phys & Appl Math, New York, NY USA
3.Beijing Computat Sci Res Ctr, Beijing, Peoples R China
4.Hong Kong Baptist Univ, Beijing Normal Univ, United Int Coll, Div Sci & Technol, Zhultai, Guangdong, Peoples R China

Yang, Jiang,Du, Qiang,Zhang, Wei. UNIFORM L-p-BOUND OF THE ALLEN-CAHN EQUATION AND ITS NUMERICAL DISCRETIZATION[J]. International Journal of Numerical Analysis and Modeling,2018,15(1-2):213-227.

Yang, Jiang,Du, Qiang,&Zhang, Wei.(2018).UNIFORM L-p-BOUND OF THE ALLEN-CAHN EQUATION AND ITS NUMERICAL DISCRETIZATION.International Journal of Numerical Analysis and Modeling,15(1-2),213-227.

Yang, Jiang,et al."UNIFORM L-p-BOUND OF THE ALLEN-CAHN EQUATION AND ITS NUMERICAL DISCRETIZATION".International Journal of Numerical Analysis and Modeling 15.1-2(2018):213-227.