A new conservative finite difference scheme for 1D Cahn-Hilliard equation coupled with elasticity

• Autorzy: Shimura Kazuki , Yoshikawa Shuji

Identyfikatory

DOI

10.1515/jaa-2021-2071

• Języki publikacji: EN

Abstrakty

EN

In this article, we give analysis for a structure-preserving finite difference scheme to the Cahn-Hilliard system coupled with elasticity in one space dimension. In the previous article [K. Shimura and S. Yoshikawa, Error estimate for structure-preserving finite difference schemes of the one-dimensional Cahn-Hilliard system coupled with viscoelasticity, in: Regularity and Asymptotic Analysis for Critical Cases of Partial Differential Equations, RIMS Kôkyûroku Bessatsu B82, Research Institute for Mathematical Sciences (RIMS), Kyoto (2020), 159-175], we studied the system coupled with viscoelasticity, where we proposed a conservative numerical scheme for the system which inherits the total energy conservation and momentum conservation laws, and showed the error estimate. However, the error estimate can not be applied to the system without viscosity, due to the fact that the proof relies on the viscous term. Here, we show the error estimate for the system without viscosity by proposing a new structure-preserving finite difference scheme for the system. In addition, we also give the proof of existence of solution for the scheme.

Słowa kluczowe

EN

phase separation; Cahn-Hilliard equation; viscoelasticity; elasticity; structure-preserving; finite difference methods

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2022
• Tom: Vol. 28, nr 2
• Strony: 311--332
• Opis fizyczny: Bibliogr. 22 poz., wykr.

Twórcy

autor

Shimura Kazuki

• Computer and Information Science, Graduate School of Engineering, Oita University, 700 Dannoharu, Oita-shi, Oita, 870-1192, Japan

autor

Yoshikawa Shuji

• Division of Mathematical Sciences, Faculty of Science and Technology, Oita University, 700 Dannoharu, Oita-shi, Oita, 870-1192, Japan

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).