Unconditionally energy stable invariant energy quadratization finite element methods for Phase-Field Crystal equation and Swift–Hohenberg equation

In this paper, we design, analyze and numerically validate linearly first- and second-order unconditionally energy stable numerical methods for solving the Phase-Field Crystal equation and Swift–Hohenberg equation which describe a multitude of processes involving spatiotemporal pattern formation. Th...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 450; p. 115996
Main Authors Wang, Hao, Chen, Yaoyao
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2024
Subjects
Energy dissipation
Finite element method
Invariant energy quadratization method
Phase-field crystal equation
Swift–Hohenberg equation
Finite element method
65N12
Invariant energy quadratization method
Energy dissipation
35K35
Phase-field crystal equation
Swift–Hohenberg equation
65N30
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Summary:In this paper, we design, analyze and numerically validate linearly first- and second-order unconditionally energy stable numerical methods for solving the Phase-Field Crystal equation and Swift–Hohenberg equation which describe a multitude of processes involving spatiotemporal pattern formation. The properties of well-posedness of solution and the decrease of the total energy for the fully discretized schemes are established. Numerical examples are presented to confirm the accuracy, efficiency, and stability of the proposed method.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2024.115996