A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations

Liao，Hong lin1; Tang，Tao2,3; Zhou，Tao4

2020-08-01

10.1016/j.jcp.2020.109473

JOURNAL OF COMPUTATIONAL PHYSICS   影响因子和分区

0021-9991

1090-2716

In this work, we present a second-order nonuniform time-stepping scheme for the time-fractional Allen-Cahn equation. We show that the proposed scheme preserves the discrete maximum principle, and by using the convolution structure of consistency error, we present sharp maximum-norm error estimates which reflect the temporal regularity. As our analysis is built on nonuniform time steps, we may resolve the intrinsic initial singularity by using the graded meshes. Moreover, we propose an adaptive time-stepping strategy for large time simulations. Numerical experiments are presented to show the effectiveness of the proposed scheme. This seems to be the first second-order maximum principle preserving scheme for the time-fractional Allen-Cahn equation.

Adaptive time-stepping strategy Alikhanov formula Discrete maximum principle Sharp error estimate Time-fractional Allen-Cahn equation

SCI ; EI

英语

ESI高被引

其他

NUAA Scientific Research Starting Fund of Introduced Talent[1008-56SYAH18037] ; NSF of China[11822111][11688101][91630203][11571351][11731006] ; Science Challenge Project[TZ2018001]

Computer Science ; Physics

Computer Science, Interdisciplinary Applications ; Physics, Mathematical

WOS:000536532800011

ACADEMIC PRESS INC ELSEVIER SCIENCE

20201708572189

Errors ; Convolution

Information Theory and Signal Processing:716.1

PHYSICS

2-s2.0-85083735866

Scopus

1.Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing,211106,China
2.Department of Mathematics,International Center for Mathematics,Southern University of Science and Technology,Shenzhen,China
3.Division of Science and Technology,BNU-HKBU United International College,Zhuhai,China
4.NCMIS,LSEC,Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing,100190,China

Liao，Hong lin,Tang，Tao,Zhou，Tao. A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2020,414.

Liao，Hong lin,Tang，Tao,&Zhou，Tao.(2020).A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations.JOURNAL OF COMPUTATIONAL PHYSICS,414.

Liao，Hong lin,et al."A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations".JOURNAL OF COMPUTATIONAL PHYSICS 414(2020).