Volume 26, Issue 5
Energy Law Preserving Finite Element Scheme for the Cahn-Hilliard Equation with Dynamic Boundary Conditions

Na Li, Ping Lin & Fuzheng Gao

Commun. Comput. Phys., 26 (2019), pp. 1490-1509.

Published online: 2019-08

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  • Abstract

In this paper, we develop the energy law preserving method for a phasefield 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.

  • Keywords

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

  • AMS Subject Headings

65M06, 76T10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

dajiena2002@163.com (Na Li)

plin@maths.dundee.ac.uk (Ping Lin)

fzgao@sdu.edu.cn (Fuzheng Gao)

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@Article{CiCP-26-1490, author = {Li , Na and Lin , Ping and Gao , Fuzheng }, title = {Energy Law Preserving Finite Element Scheme for the Cahn-Hilliard Equation with Dynamic Boundary Conditions}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {5}, pages = {1490--1509}, abstract = {

In this paper, we develop the energy law preserving method for a phasefield 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2019.js60.14}, url = {http://global-sci.org/intro/article_detail/cicp/13273.html} }
TY - JOUR T1 - Energy Law Preserving Finite Element Scheme for the Cahn-Hilliard Equation with Dynamic Boundary Conditions AU - Li , Na AU - Lin , Ping AU - Gao , Fuzheng JO - Communications in Computational Physics VL - 5 SP - 1490 EP - 1509 PY - 2019 DA - 2019/08 SN - 26 DO - http://dor.org/10.4208/cicp.2019.js60.14 UR - https://global-sci.org/intro/cicp/13273.html KW - Cahn-Hilliard equation, dynamic boundary condition, energy law preservation, finite element method. AB -

In this paper, we develop the energy law preserving method for a phasefield 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.

Na Li, Ping Lin & Fuzheng Gao. (2019). Energy Law Preserving Finite Element Scheme for the Cahn-Hilliard Equation with Dynamic Boundary Conditions. Communications in Computational Physics. 26 (5). 1490-1509. doi:10.4208/cicp.2019.js60.14
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