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A Linear, Second-Order, and Unconditionally Energy-Stable Method for the L 2 -Gradient Flow-Based Phase-Field Crystal Equation

Author

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  • Hyun Geun Lee

    (Department of Mathematics, Kwangwoon University, Seoul 01897, Korea)

Abstract

To solve the L 2 -gradient flow-based phase-field crystal equation accurately and efficiently, we present a linear, second-order, and unconditionally energy-stable method. We first truncate the quartic function in the Swift–Hohenberg energy functional. We also put the truncated function in the expansive part of the energy and add an extra term to have a linear convex splitting. Then, we apply the linear convex splitting to both the L 2 -gradient flow and the nonlocal Lagrange multiplier terms and combine it with the second-order SSP-IMEX-RK method. We prove that the proposed method is mass-conservative and unconditionally energy-stable. Numerical experiments including standard tests in the classical H − 1 -gradient flow-based phase-field crystal equation support that the proposed method is second-order accurate in time, mass conservative, and unconditionally energy-stable.

Suggested Citation

  • Hyun Geun Lee, 2022. "A Linear, Second-Order, and Unconditionally Energy-Stable Method for the L 2 -Gradient Flow-Based Phase-Field Crystal Equation," Mathematics, MDPI, vol. 10(4), pages 1-9, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:548-:d:746116
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    References listed on IDEAS

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    1. Xiaowei Chen & Mingzhan Song & Songhe Song, 2020. "A Fourth Order Energy Dissipative Scheme for a Traffic Flow Model," Mathematics, MDPI, vol. 8(8), pages 1-10, July.
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