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Title: Characterizing the stabilization size for semi-implicit fourier-spectral method to phase field equations
Authors: Li, D
Qiao, Z 
Tang, T
Issue Date: 2016
Source: SIAM journal on numerical analysis, 2016, v. 54, no. 3, p. 1653-1681
Abstract: Recent results in the literature provide computational evidence that the stabilized semi-implicit time-stepping method can eficiently simulate phase field problems involving fourth order nonlinear diffusion, with typical examples like the Cahn-Hilliard equation and the thin film type equation. The up-to-date theoretical explanation of the numerical stability relies on the assumption that the derivative of the nonlinear potential function satisfies a Lipschitz-type condition, which in a rigorous sense, implies the boundedness of the numerical solution. In this work we remove the Lipschitz assumption on the nonlinearity and prove unconditional energy stability for the stabilized semi-implicit time-stepping methods. It is shown that the size of the stabilization term depends on the initial energy and the perturbation parameter but is independent of the time step. The corresponding error analysis is also established under minimal nonlinearity and regularity assumptions.
Keywords: Cahn-Hilliard
Energy stable
Epitaxy
Large time stepping
Thin film
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on numerical analysis 
ISSN: 0036-1429
DOI: 10.1137/140993193
Rights: © 2016 Society for Industrial and Applied Mathematics
The following publication Li, D., Qiao, Z., & Tang, T. (2016). Characterizing the stabilization size for semi-implicit Fourier-spectral method to phase field equations. SIAM Journal on Numerical Analysis, 54(3), 1653-1681 is available at https://doi.org/10.1137/140993193
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