Abstract
In this article we consider the numerical analysis of the Cahn–Hilliard equation in a bounded domain with non-permeable walls, endowed with dynamic-type boundary conditions. The dynamic-type boundary conditions that we consider here have been recently proposed in Ruiz Goldstein et al. (Phys D 240(8):754–766, 2011) in order to describe the interactions of a binary material with the wall. The equation is semi-discretized using a finite element method for the space variables and error estimates between the exact and the approximate solution are obtained. We also prove the stability of a fully discrete scheme based on the backward Euler scheme for the time discretization. Numerical simulations sustaining the theoretical results are presented.
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The authors would like to thank Professor Alain Miranville for suggesting this problem, as well as for fruitful discussions.
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Cherfils, L., Petcu, M. A numerical analysis of the Cahn–Hilliard equation with non-permeable walls. Numer. Math. 128, 517–549 (2014). https://doi.org/10.1007/s00211-014-0618-0
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DOI: https://doi.org/10.1007/s00211-014-0618-0