Energy Law Preserving Finite Element Scheme for the Cahn-Hilliard Equation with Dynamic Boundary Conditions

Energy Law Preserving Finite Element Scheme for the Cahn-Hilliard Equation with Dynamic Boundary Conditions

Year:    2019

Author:    Na Li, Ping Lin, Fuzheng Gao

Communications in Computational Physics, Vol. 26 (2019), Iss. 5 : pp. 1490–1509

Abstract

In this paper, we develop the energy law preserving method for a phase-field model of Cahn-Hilliard type describing binary mixtures. A new class of dynamic boundary conditions in a rather general setting proposed in [1] is adopted here. The model equations are discretized by a continuous finite element method in space and a midpoint scheme in time. The discrete energy law of the numerical method for the model with the dynamic boundary conditions is derived. By a few two-phase examples, we demonstrate the performance of the energy law preserving method for the computation of the phase-field model with the new class of dynamic boundary conditions, even in the case of relatively coarse mesh.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.2019.js60.14

Communications in Computational Physics, Vol. 26 (2019), Iss. 5 : pp. 1490–1509

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Cahn-Hilliard equation dynamic boundary condition energy law preservation finite element method.

Author Details

Na Li

Ping Lin

Fuzheng Gao

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