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First and second order numerical methods based on a new convex splitting for phase-field crystal equation

Title
First and second order numerical methods based on a new convex splitting for phase-field crystal equation
Authors
Shin J.Lee H.G.Lee J.-Y.
Ewha Authors
이준엽
SCOPUS Author ID
이준엽scopus
Issue Date
2016
Journal Title
Journal of Computational Physics
ISSN
0021-9991JCR Link
Citation
vol. 327, pp. 519 - 542
Keywords
Convex splitting methodEnergy stabilityGradient stabilityPhase-field crystal equationSwift–Hohenberg functional
Publisher
Academic Press Inc.
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
The phase-field crystal equation derived from the Swift–Hohenberg energy functional is a sixth order nonlinear equation. We propose numerical methods based on a new convex splitting for the phase-field crystal equation. The first order convex splitting method based on the proposed splitting is unconditionally gradient stable, which means that the discrete energy is non-increasing for any time step. The second order scheme is unconditionally weakly energy stable, which means that the discrete energy is bounded by its initial value for any time step. We prove mass conservation, unique solvability, energy stability, and the order of truncation error for the proposed methods. Numerical experiments are presented to show the accuracy and stability of the proposed splitting methods compared to the existing other splitting methods. Numerical tests indicate that the proposed convex splitting is a good choice for numerical methods of the phase-field crystal equation. © 2016 Elsevier Inc.
DOI
10.1016/j.jcp.2016.09.053
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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