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arXiv · 1410.7541

Characterizing the stabilization size for semi-implicit Fourier-spectral method to phase field equations

Dong Li·Zhonghua Qiao·Tao Tang
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Abstract

Recent results in the literature provide computational evidence that stabilized semi-implicit time-stepping method can efficiently simulate phase field problems involving fourth-order nonlinear dif- fusion, 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 deriva- tive 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 stabilization term depends on the initial energy and the perturba- tion parameter but is independent of the time step. The corresponding error analysis is also established under minimal nonlinearity and regularity assumptions.

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Dong Li, Zhonghua Qiao, Tao Tang. 2014-10-28. Characterizing the stabilization size for semi-implicit Fourier-spectral method to phase field equations. https://arxiv.org/abs/1410.7541

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