Convergence of a finite-volume scheme for the Cahn-Hilliard equation with dynamic boundary conditions

Flore Nabet

doi:10.1093/imanum/drv057

Convergence of a finite-volume scheme for the Cahn-Hilliard equation with dynamic boundary conditions

Flore Nabet

Université de Provence

Research output: Contribution to journal › Article › peer-review

Abstract

This work is devoted to the numerical study of the Cahn-Hilliard equation with dynamic boundary conditions. A spatial finite-volume discretization is proposed, which couples a two-dimensional method in a smooth connected domain and a one-dimensional method on its boundary. The convergence of the sequence of approximate solutions is proved and various numerical simulations are given.

Original language	English
Pages (from-to)	1898-1942
Number of pages	45
Journal	IMA Journal of Numerical Analysis
Volume	36
Issue number	4
DOIs	https://doi.org/10.1093/imanum/drv057
Publication status	Published - 1 Oct 2016
Externally published	Yes

Keywords

Cahn-Hilliard equation
convergence analysis
dynamic boundary conditions
finite-volume method

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10.1093/imanum/drv057

Cite this

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title = "Convergence of a finite-volume scheme for the Cahn-Hilliard equation with dynamic boundary conditions",

abstract = "This work is devoted to the numerical study of the Cahn-Hilliard equation with dynamic boundary conditions. A spatial finite-volume discretization is proposed, which couples a two-dimensional method in a smooth connected domain and a one-dimensional method on its boundary. The convergence of the sequence of approximate solutions is proved and various numerical simulations are given.",

keywords = "Cahn-Hilliard equation, convergence analysis, dynamic boundary conditions, finite-volume method",

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AU - Nabet, Flore

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N2 - This work is devoted to the numerical study of the Cahn-Hilliard equation with dynamic boundary conditions. A spatial finite-volume discretization is proposed, which couples a two-dimensional method in a smooth connected domain and a one-dimensional method on its boundary. The convergence of the sequence of approximate solutions is proved and various numerical simulations are given.

AB - This work is devoted to the numerical study of the Cahn-Hilliard equation with dynamic boundary conditions. A spatial finite-volume discretization is proposed, which couples a two-dimensional method in a smooth connected domain and a one-dimensional method on its boundary. The convergence of the sequence of approximate solutions is proved and various numerical simulations are given.

KW - Cahn-Hilliard equation

KW - convergence analysis

KW - dynamic boundary conditions

KW - finite-volume method

UR - https://www.scopus.com/pages/publications/84990890548

U2 - 10.1093/imanum/drv057

DO - 10.1093/imanum/drv057

M3 - Article

AN - SCOPUS:84990890548

SN - 0272-4979

VL - 36

SP - 1898

EP - 1942

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

IS - 4

ER -

Convergence of a finite-volume scheme for the Cahn-Hilliard equation with dynamic boundary conditions

Abstract

Keywords

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