Abstract
In this paper, a second-order accurate (in time) energy stable Fourier spectral scheme for the fractional-in-space Cahn-Hilliard (CH) equation is considered. The time is discretized by the implicit backward differentiation formula (BDF), along with a linear stabilized term which represents a second-order Douglas-Dupont-type regularization. The semidiscrete schemes are shown to be energy stable and to be mass conservative. Then we further use Fourier-spectral methods to discretize the space. Some numerical examples are included to testify the effectiveness of our proposed method. In addition, it shows that the fractional order controls the thickness and the lifetime of the interface, which is typically diffusive in integer order case.
Highlights
The Cahn-Hilliard model [1, 2] was originated from a phaseseparation model in a binary alloy
We focus on the following fractional-inspace Cahn-Hilliard (CH) equation [9]:
We have presented a second order backward differentiation formula (BDF)-type scheme in time to solve fractional-in-space CH model
Summary
The Cahn-Hilliard model [1, 2] was originated from a phaseseparation model in a binary alloy. It is important to study the physical properties of Cahn-Hilliard equations by accurate and efficient numerical algorithms. Bosch and Stoll [8] used Fourier spectral method for fractional vector-valued CH model combined with an implicit first-order convex splitting scheme. Weng [11] et al proposed an unconditionally energy stable nonlinear Fourier spectral scheme for model (1) by introducing a stabilizing term. In our previous work [11], we have proposed second-order unconditionally energy stable Fourier spectral scheme for fractional-in-space Cahn-Hilliard equation using the CrankNicolson methodology and nonlinear stabilized term. Compared with the literature [11], our method is more efficient for solving fractional-in-space Cahn-Hilliard in numerical experiments.
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