Energy Law Preserving Finite Element Scheme for the Cahn-Hilliard Equation with Dynamic Boundary Conditions (Communications in Computational Physics, 2019)
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 dynamicboundary conditions in a rather general setting proposed in [1] is adopted here. Themodel equations are discretized by a continuous finite element method in space anda midpoint scheme in time. The discrete energy law of the numerical method for themodel with the dynamic boundary conditions is derived. By a few two-phase examples, we demonstrate the performance of the energy law preserving method for thecomputation 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.