<abstract xmlns="http://www.w3.org/1999/xhtml">
<p>This paper focuses on the complex version of the Cahn-Hilliard-Oono equation with Neumann boundary conditions, which is used to capture long-range nonlocal interactions in the phase separation process. The first part of the paper establishes the well-posedness of the corresponding stationary problem associated with the equation. Subsequently, a numerical model is constructed using a finite element discretization in space and a backward Euler scheme in time. We demonstrate the existence of a unique solution to the stationary problem and obtain error estimates for the numerical solution. This, in turn, serves as proof of the convergence of the semi-discrete scheme to the continuous problem. Finally, we establish the convergence of the fully discrete problem to the semi-discrete formulation.</p>
</abstract>

This paper focuses on the complex version of the Cahn-Hilliard-Oono equation with Neumann boundary conditions, which is used to capture long-range nonlocal interactions in the phase separation process. The first part of the paper establishes the well-posedness of the corresponding stationary problem associated with the equation. Subsequently, a numerical model is constructed using a finite element discretization in space and a backward Euler scheme in time. We demonstrate the existence of a unique solution to the stationary problem and obtain error estimates for the numerical solution. This, in turn, serves as proof of the convergence of the semi-discrete scheme to the continuous problem. Finally, we establish the convergence of the fully discrete problem to the semi-discrete formulation.

On the complex version of the Cahn–Hilliard–Oono type equation for long interactions phase separation

Khawarizmi Laboratory for Mathematics and Applications

Faculty of Engineering, Department of Preparatory Classes

International Journal of Mathematics and Computer in Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

This paper focuses on the complex version of the Cahn-Hilliard-Oono equation with Neumann boundary conditions, which is used to capture long-range nonlocal...

On the complex version of the Cahn–Hilliard–Oono type equation for long interactions phase separation

Article Category: Original Study

Published Online: Jan 10, 2024

Page range: 233 - 250

Received: Aug 18, 2023

Accepted: Nov 16, 2023

DOI: https://doi.org/10.2478/ijmce-2024-0018

Keywords
Nonlocal Cahn–Hilliard–Oono, well-posedness, steady-state solution, numerical analysis, finite element, phase separation

© 2024 Hussein Fakih et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

On the complex version of the Cahn–Hilliard–Oono type equation for long interactions phase separation

Article Category: Original Study

Published Online: Jan 10, 2024

Page range: 233 - 250

Received: Aug 18, 2023

Accepted: Nov 16, 2023

DOI: https://doi.org/10.2478/ijmce-2024-0018

KeywordsNonlocal Cahn–Hilliard–Oono, well-posedness, steady-state solution, numerical analysis, finite element, phase separation

© 2024 Hussein Fakih et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Nonlocal Cahn–Hilliard–Oono, well-posedness, steady-state solution, numerical analysis, finite element, phase separation