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Volume 19, Issue 5
A Numerical Analysis of the Coupled Cahn-Hilliard/Allen-Cahn System with Dynamic Boundary Conditions

Ahmad Makki, Alain Miranville & Madalina Petcu

Int. J. Numer. Anal. Mod., 19 (2022), pp. 630-655.

Published online: 2022-08

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  • 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.

  • Keywords

Cahn-Hilliard/Allen-Cahn equations, dynamic boundary conditions, finite element method, error estimates, backward Euler scheme, Lojasiewicz inequality.

  • AMS Subject Headings

65M60, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-630, author = {Makki , AhmadMiranville , Alain and Petcu , Madalina}, title = {A Numerical Analysis of the Coupled Cahn-Hilliard/Allen-Cahn System with Dynamic Boundary Conditions }, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {5}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20930.html} }
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 -

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.

Makki , AhmadMiranville , Alain and Petcu , Madalina. (2022). A Numerical Analysis of the Coupled Cahn-Hilliard/Allen-Cahn System with Dynamic Boundary Conditions . International Journal of Numerical Analysis and Modeling. 19 (5). 630-655. doi:
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