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

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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.

eISSN:
2956-7068
Lingua:
Inglese
Frequenza di pubblicazione:
2 volte all'anno
Argomenti della rivista:
Computer Sciences, other, Engineering, Introductions and Overviews, Mathematics, General Mathematics, Physics