| Abstract: |
| Recently, the Cahn-Hilliard equation with new dynamical boundary conditions has been proposed by Liu and Wu. This model has characteristic conservation laws in that each mass of the interior of the domain and the boundary are conserved. In addition, the total energy dissipation law, which represents that the sum of energy in bulk and on the boundary decreases, holds in this model. From the perspective of numerical computation, the properties often lead us to stable computation. Hence, if the designed schemes retain the properties in a discrete sense, then the schemes are expected to be stable. In this study, In this study, we consider the Liu-Wu model in a two-dimensional rectangular domain with periodic boundary conditions on the left and right boundaries and dynamic boundary conditions on the upper and lower boundaries. Then, we propose a structure-preserving scheme for this model that retains the aforementioned conservation and dissipation laws in a discrete sense. Also, we will talk about the proof of the solvability of the proposed scheme and show the results of numerical computations in the presentation. |
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