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http://hdl.handle.net/10397/61867
| 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 |
| Appears in Collections: | Journal/Magazine Article |
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