Abstract
We study space and time discretizations of a Cahn–Hilliard type equation with dynamic boundary conditions. We first study a semi-discrete version of the equation and we prove optimal error estimates in energy norms and weaker norms. Then, we study the stability of the fully discrete scheme obtained by applying the Euler backward scheme to the space semi-discrete problem. In particular, we show that this fully discrete problem is unconditionally stable. Some numerical results in two space dimensions conclude the paper.
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Communicated by Salvatore Rionero.
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Israel, H., Miranville, A. & Petcu, M. Numerical analysis of a Cahn–Hilliard type equation with dynamic boundary conditions. Ricerche mat. 64, 25–50 (2015). https://doi.org/10.1007/s11587-014-0187-7
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DOI: https://doi.org/10.1007/s11587-014-0187-7