Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system

Zheng, Nan; Li, Xiaoli

doi:10.1007/s10444-021-09897-0

Cited by 11 publications

(1 citation statement)

References 21 publications

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“…In this paper, we assume the periodic boundary condition and focus on time and space discretization. Therefore, we use the Fourier spectral method [ 7 , 8 ] for the spatial discretization for the system. In recent decades, many scholars focus on the numerical solution for the MPFC model and have conducted extensive related works and proposed various time-marching methods.…”

Section: Introductionmentioning

confidence: 99%

A Second-Order Crank–Nicolson Leap-Frog Scheme for the Modified Phase Field Crystal Model with Long-Range Interaction

Feng

Qian

2022

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In this paper, we construct a fully discrete and decoupled Crank–Nicolson Leap-Frog (CNLF) scheme for solving the modified phase field crystal model (MPFC) with long-range interaction. The idea of CNLF is to treat stiff terms implicity with Crank–Nicolson and to treat non-stiff terms explicitly with Leap-Frog. In addition, the scalar auxiliary variable (SAV) method is used to allow explicit treatment of the nonlinear potential, then, these technique combines with CNLF can lead to the highly efficient, fully decoupled and linear numerical scheme with constant coefficients at each time step. Furthermore, the Fourier spectral method is used for the spatial discretization. Finally, we show that the CNLF scheme is fully discrete, second-order decoupled and unconditionally stable. Ample numerical experiments in 2D and 3D are provided to demonstrate the accuracy, efficiency, and stability of the proposed method.

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Section: Introductionmentioning

confidence: 99%