Fully decoupled SAV Fourier-spectral scheme for the Cahn–Hilliard–Hele–Shaw system

In this paper, we construct first- and second-order fully discrete schemes for the Cahn–Hilliard–Hele–Shaw system based on the Fourier-spectral method for spatial discretization. For temporal discretization, we combine two efficient approaches, including the scalar auxiliary variable (SAV) method fo...

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Bibliographic Details
Main Authors: Linhui Zhang, Hongen Jia, Hongbin Wang
Format: Article
Language:English
Published: Elsevier 2025-02-01
Series:Results in Applied Mathematics
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Online Access:http://www.sciencedirect.com/science/article/pii/S2590037424001043
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Summary:In this paper, we construct first- and second-order fully discrete schemes for the Cahn–Hilliard–Hele–Shaw system based on the Fourier-spectral method for spatial discretization. For temporal discretization, we combine two efficient approaches, including the scalar auxiliary variable (SAV) method for linearizing nonlinear potentials and the zero-energy-contribution method (ZEC) for decoupling nonlinear couplings. These schemes are linear, fully decoupled, and unconditionally energy stable, requiring only the solution of a sequence of elliptic equations with constant coefficients at each time step. The rigorous proof of the error analysis for the first-order scheme is shown. In addition, several numerical examples are presented to demonstrate the stability, accuracy, and efficiency of the proposed scheme.
ISSN:2590-0374