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

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.

Author Details

Ahmad Makki

Alain Miranville

Madalina Petcu