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://doi.org/10.4208/cicp.2019.js60.14 UR - https://global-sci.org/intro/article_detail/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 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.