Unconditionally energy stable invariant energy quadratization finite element methods for Phase-Field Crystal equation and Swift–Hohenberg equation (2024)

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Authors: Hao Wang, Yaoyao Chen

Published: 08 August 2024 Publication History

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    Abstract

    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.

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    Published In

    Unconditionally energy stable invariant energy quadratization finite element methods for Phase-Field Crystal equation and Swift–Hohenberg equation (1)

    Journal of Computational and Applied Mathematics Volume 450, Issue C

    Nov 2024

    429 pages

    ISSN:0377-0427

    Issue’s Table of Contents

    Elsevier B.V.

    Publisher

    Elsevier Science Publishers B. V.

    Netherlands

    Publication History

    Published: 08 August 2024

    Author Tags

    1. 65N12
    2. 65N30
    3. 35K35

    Author Tags

    1. Phase-field crystal equation
    2. Swift–Hohenberg equation
    3. Invariant energy quadratization method
    4. Finite element method
    5. Energy dissipation

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    Unconditionally energy stable invariant energy quadratization finite element methods for Phase-Field Crystal equation and Swift–Hohenberg equation (2)

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