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A stabilized fully-discrete scheme for phase field crystal equation
Zhang, Fan1; Li, Dongfang2,3; Sun, Hai Wei1; Zhang, Jia Li1
2022-08-01
Source PublicationApplied Numerical Mathematics
ISSN0168-9274
Volume178Pages:337-355
Abstract

A finite difference scheme is developed for solving the phase field crystal equation with the Dirichlet boundary condition. The second-order stabilized semi-implicit scheme is applied to discretize the time variable. The mass conservation, unique solvability of the semi-discrete scheme are proved. Then, the spatial discretization is attained by the fourth-order compact difference scheme. The unconditional energy stability and convergence analysis of the fully-discrete scheme are presented. In the implementation, a fast sine transform technique is utilized to reduce the computational cost. Several numerical examples are presented to verify the effectiveness of the proposed scheme.

KeywordCompact Difference Scheme Crank-nicolson/adams-bashforth Scheme Energy Stability Error Estimate Phase Field Crystal Equation
DOI10.1016/j.apnum.2022.04.007
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000797248100006
Scopus ID2-s2.0-85128936472
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorLi, Dongfang; Sun, Hai Wei
Affiliation1.Department of Mathematics, University of Macau, Macao
2.School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China
3.Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, China
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Zhang, Fan,Li, Dongfang,Sun, Hai Wei,et al. A stabilized fully-discrete scheme for phase field crystal equation[J]. Applied Numerical Mathematics,2022,178:337-355.
APA Zhang, Fan,Li, Dongfang,Sun, Hai Wei,&Zhang, Jia Li.(2022).A stabilized fully-discrete scheme for phase field crystal equation.Applied Numerical Mathematics,178,337-355.
MLA Zhang, Fan,et al."A stabilized fully-discrete scheme for phase field crystal equation".Applied Numerical Mathematics 178(2022):337-355.
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