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

Autor:	Kazuki Shimura, Shuji Yoshikawa
Rok vydání:	2022
Předmět:	Computational Theory and Mathematics Applied Mathematics Phase separation elasticity structure-preserving Statistics Probability and Uncertainty finite difference methods viscoelasticity Mathematical Physics Cahn-Hilliard equation
Zdroj:	Journal of Applied Analysis. 28:311-332
ISSN:	1869-6082 1425-6908
DOI:	10.1515/jaa-2021-2071
Popis:	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, 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cf358395fea1e41ccb216eac6237dba2 https://doi.org/10.1515/jaa-2021-2071 Zobrazit plný text záznamu