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• W3042770731 abstract "We propose a structure-preserving finite difference scheme for the Cahn-Hilliard equation with a dynamic boundary condition using the discrete variational derivative method (DVDM). In this approach, it is important and essential how to discretize the energy which characterizes the equation. By modifying the conventional manner and using an appropriate summation-by-parts formula, we can use a standard central difference operator as an approximation of an outward normal derivative on the discrete boundary condition of the scheme. We show that our proposed scheme is second-order accurate in space, although the previous structure-preserving scheme by Fukao-Yoshikawa-Wada (Commun. Pure Appl. Anal. 16 (2017), 1915-1938) is first-order accurate in space. Also, we show the stability, the existence, and the uniqueness of the solution for the proposed scheme. Computation examples demonstrate the effectiveness of the proposed scheme. Especially through computation examples, we confirm that numerical solutions can be stably obtained by our proposed scheme." @default.
• W3042770731 created "2020-07-23" @default.
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• W3042770731 date "2020-07-16" @default.
• W3042770731 modified "2023-09-26" @default.
• W3042770731 title "A second-order accurate structure-preserving scheme for the Cahn-Hilliard equation with a dynamic boundary condition" @default.
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• W3042770731 doi "https://doi.org/10.48550/arxiv.2007.08355" @default.
• W3042770731 hasPublicationYear "2020" @default.
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