Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions

05/07/2020

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by   Paula Harder, et al.

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A proof of convergence is given for bulk–surface finite element semi-discretisation of the Cahn–Hilliard equation with Cahn–Hilliard-type dynamic boundary conditions in a smooth domain. The semi-discretisation is studied in the weak formulation as a second order system. Optimal-order uniform-in-time error estimates are shown in the L^2 and H^1 norms. The error estimates are based on a consistency and stability analysis. The proof of stability is performed in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second order system. Numerical experiments illustrate the theoretical results.