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

Hyun Geun Lee
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Hyun Geun Lee: Department of Mathematics, Kwangwoon University, Seoul 01897, Korea

Mathematics, 2022, vol. 10, issue 4, 1-9

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.

Keywords: L 2 -gradient flow-based phase-field crystal equation; linear convex splitting; SSP-IMEX-RK method; mass conservation; unconditional energy stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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