A numerical analysis of the Cahn-Hilliard equation with non-permeable walls

作者：Cherfils Laurence; Petcu Madalina^*

来源：Numerische Mathematik, 2014, 128(3): 517-549.

DOI：10.1007/s00211-014-0618-0

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.

• 出版日期2014-11