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

被引：140

作者：

Liao, Hong-lin ^{[1
]}

Tang, Tao ^{[2
,3
,4
]}

Zhou, Tao ^{[5
,6
]}

机构：

[1] Nanjing Univ Aeronut & Astronaut, Dept Math, Nanjing 211106, Peoples R China

[2] Southern Univ Sci & Technol, Dept Math, Shenzhen, Guangdong, Peoples R China

[3] Southern Univ Sci & Technol, Int Ctr Math, Shenzhen, Guangdong, Peoples R China

[4] BNU HKBU United Int Coll, Div Sci & Technol, Zhuhai, Guangdong, Peoples R China

[5] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS, Beijing 100190, Peoples R China

[6] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2020年 / 414卷

关键词：

Time-fractional Allen-Cahn equation; Alikhanov formula; Adaptive time-stepping strategy; Discrete maximum principle; Sharp error estimate; NUMERICAL-ANALYSIS; DIFFERENCE SCHEME; HILLIARD; STRATEGY; APPROXIMATIONS; STABILITY; ACCURATE;

D O I：

10.1016/j.jcp.2020.109473

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

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. (c) 2020 Elsevier Inc. All rights reserved.

引用

页数：16

共 32 条

[1] A new difference scheme for the time fractional diffusion equation [J].

Alikhanov, Anatoly A. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 280 :424-438

[2] MICROSCOPIC THEORY FOR ANTIPHASE BOUNDARY MOTION AND ITS APPLICATION TO ANTIPHASE DOMAIN COARSENING [J].

ALLEN, SM ;

CAHN, JW .

ACTA METALLURGICA, 1979, 27 (06) :1085-1095

[3] Error Analysis of a Second-Order Method on Fitted Meshes for a Time-Fractional Diffusion Problem [J].

Chen, Hu ;

Stynes, Martin .

JOURNAL OF SCIENTIFIC COMPUTING, 2019, 79 (01) :624-647

[4]

Chen MH, 2019, INT J NUMER ANAL MOD, V16, P297

[5] Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows [J].

Feng, XB ;

Prohl, A .

NUMERISCHE MATHEMATIK, 2003, 94 (01) :33-65

[6] Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models [J].

Gomez, Hector ;

Hughes, Thomas J. R. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 230 (13) :5310-5327

[7] Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations [J].

Guan, Zhen ;

Lowengrub, John S. ;

Wang, Cheng ;

Wise, Steven M. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 277 :48-71

[8] A High Order Adaptive Time-Stepping Strategy an d Local Discontinuous Galerkin Method for the Modified Phase Field Crystal Equation [J].

Guo, Ruihan ;

Xu, Yan .

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2018, 24 (01) :123-151

[9] Numerical Analysis of Fully Discretized Crank-Nicolson Scheme for Fractional-in-Space Allen-Cahn Equations [J].

Hou, Tianliang ;

Tang, Tao ;

Yang, Jiang .

JOURNAL OF SCIENTIFIC COMPUTING, 2017, 72 (03) :1214-1231

[10] Time-fractional Cahn-Allen and time-fractional Klein-Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis [J].

Inc, Mustafa ;

Yusuf, Abdullahi ;

Aliyu, Aliyu Isa ;

Baleanu, Dumitru .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2018, 493 :94-106

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