A structure-preserving and variable-step BDF2 Fourier pseudo-spectral method for the two-mode phase field crystal model

Dongfang Li, Xiaoxi Li, Ming Mei and Wanqiu Yuan

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 205, issue C, 483-506

Abstract: For the two-mode phase field crystal models, the evolutions of the solutions and energy vary fast at certain time. To resolve varying time scales efficiently and reduce the computational cost, a variable-step BDF2 Fourier pseudo-spectral method is proposed. It is shown that the fully-discrete scheme is volume-conserving and unconditional energy-stable. Moreover, a robust error estimate is established by using the discrete orthogonal convolution kernels and the corresponding convolution inequalities. Numerical experiments by using the random and adaptive time-stepping strategies are presented to confirm the effectiveness of the scheme.

Keywords: Variable-step BDF2 scheme; Two-mode phase-field crystal model; Robust L2 error estimate; Structure-preserving (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:205:y:2023:i:c:p:483-506

DOI: 10.1016/j.matcom.2022.10.009

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