A Numerical Analysis of the Coupled Cahn-Hilliard/Allen-Cahn System with Dynamic Boundary Conditions

Abstract

The numerical analysis of the coupled Cahn-Hilliard/Allen-Cahn system endowed with dynamic boundary conditions is studied in this article. We consider a semi-discretisation in space using a finite element method and we derive error estimates between the exact and the approximate solution. Then, using the backward Euler scheme for the time variable, a fully discrete scheme is obtained and its stability is proved. Some numerical simulations illustrate the behavior of the solution under the influence of dynamical boundary conditions.