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

Na Li ,  Ping Lin and Fuzheng Gao

10.4208/cicp.2019.js60.14

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

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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.

  • History

Published online: 2019-08

  • AMS Subject Headings

65M06, 76T10

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