TY - JOUR
T1 - A Numerical Analysis of the Coupled Cahn-Hilliard/Allen-Cahn System with Dynamic Boundary Conditions 
AU - Makki , Ahmad
AU - Miranville , Alain
AU - Petcu , Madalina
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 630
EP - 655
PY - 2022
DA - 2022/08
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/20930.html
KW - Cahn-Hilliard/Allen-Cahn equations, dynamic boundary conditions, finite element method, error estimates, backward Euler scheme, Lojasiewicz inequality.
AB - <p style="text-align: justify;">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.</p>