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Finite element approximation of coupled Cahn-Hilliard equations with a logarithmic potential and nondegenerate mobility | ||
| Journal of Mathematical Modeling | ||
| مقاله 16، دوره 13، شماره 1، خرداد 2025، صفحه 49-68 اصل مقاله (7.18 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2024.26657.2347 | ||
| نویسندگان | ||
| Ghufran A. Al-Musawi1؛ Akil J. Harfash* 2 | ||
| 1Department of Mathematics, College of Sciences, University of Basrah, Basrah, Iraq & Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq | ||
| 2Department of Mathematics, College of Sciences, University of Basrah, Basrah, Iraq | ||
| چکیده | ||
| This research presents a numerical analysis conducted on a system of coupled Cahn-Hilliard equations featuring a logarithmic potential, nondegenerate mobility, and homogeneous Neumann boundary conditions. These equations are derived from a model describing phase separation in a thin film of binary liquid mixture. The study proposes semi-discrete and fully-discrete piecewise linear finite element approximations to the continuous problem. Existence, uniqueness, and various stability estimates for the approximate solutions are established. Fully-discrete error bounds are derived, and optimal time discretisation error is demonstrated. An iterative method is introduced for solving the resulting nonlinear algebraic system, and linear stability analysis in one space dimension is investigated. The research concludes with numerical experiments, providing illustrations of some of the theoretical findings, conducted in both one and two space dimensions. | ||
| کلیدواژهها | ||
| Semi-discrete؛ logarithmic potential؛ finite element؛ weak formulation؛ error bounds | ||
| مراجع | ||
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