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Mathematics > Numerical Analysis

arXiv:1812.09486 (math)
[Submitted on 22 Dec 2018 (v1), last revised 25 May 2020 (this version, v2)]

Title:High-order energy stable schemes of incommensurate phase-field crystal model

Authors:Kai Jiang, Wei Si
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Abstract:This article focuses on the development of high-order energy stable schemes for the multi-length-scale incommensurate phase-field crystal model which is able to study the phase behavior of aperiodic structures. These high-order schemes based on the scalar auxiliary variable (SAV) and spectral deferred correction (SDC) approaches are suitable for the L 2 gradient flow equation, i.e., the Allen-Cahn dynamic equation. Concretely, we propose a second-order Crank-Nicolson (CN) scheme of the SAV system, prove the energy dissipation law, and give the error estimate in the almost periodic function sense. Moreover, we use the SDC method to improve the computational accuracy of the SAV/CN scheme. Numerical results demonstrate the advantages of high-order numerical methods in numerical computations and show the influence of length-scales on the formation of ordered structures.
Comments: 22 pages, 6 figures
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1812.09486 [math.NA]
  (or arXiv:1812.09486v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1812.09486

Submission history

From: Kai Jiang [view email]
[v1] Sat, 22 Dec 2018 09:33:33 UTC (879 KB)
[v2] Mon, 25 May 2020 05:45:45 UTC (2,313 KB)
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