A Numerical Analysis of the Coupled Cahn-Hilliard/Allen-Cahn System with Dynamic Boundary Conditions
Year: 2022
Author: Ahmad Makki, Alain Miranville, Madalina Petcu
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 5 : pp. 630–655
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2022-IJNAM-20930
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 5 : pp. 630–655
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Cahn-Hilliard/Allen-Cahn equations dynamic boundary conditions finite element method error estimates backward Euler scheme Lojasiewicz inequality.