C++ framework EconDrop: An efficient and convergent finite element scheme for Cahn-Hilliard equations with dynamic boundary conditions. The Cahn-Hilliard equation is a widely used model that describes among others phase-separation processes of binary mixtures or two-phase flows. In recent years, different types of boundary conditions for the Cahn-Hilliard equation were proposed and analyzed. In this publication, we are concerned with the numerical treatment of a recent model which introduces an additional Cahn-Hilliard type equation on the boundary as closure for the Cahn-Hilliard equation in the domain [C. Liu and H. Wu, Arch. Ration. Mech. Anal., 233 (2019), pp. 167-247]. By identifying a mapping between the phase-field parameter and the chemical potential inside of the domain, we are able to postulate an efficient, unconditionally energy stable finite element scheme. Furthermore, we establish the convergence of discrete solutions toward suitable weak solutions of the original model. This serves also as an additional pathway to establish existence of weak solutions. Furthermore, we present simulations underlining the practicality of the proposed scheme and investigate its experimental order of convergence.
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References in zbMATH (referenced in 5 articles )
Showing results 1 to 5 of 5.
- Bao, Xuelian; Zhang, Hui: Numerical approximations and error analysis of the Cahn-Hilliard equation with reaction rate dependent dynamic boundary conditions (2021)
- Knopf, Patrik; Lam, Kei Fong; Liu, Chun; Metzger, Stefan: Phase-field dynamics with transfer of materials: the Cahn-Hilliard equation with reaction rate dependent dynamic boundary conditions (2021)
- Metzger, Stefan: An efficient and convergent finite element scheme for Cahn-Hilliard equations with dynamic boundary conditions (2021)
- Knopf, Patrik; Lam, Kei Fong: Convergence of a Robin boundary approximation for a Cahn-Hilliard system with dynamic boundary conditions (2020)
- Gaute Linga, Asger Bolet, Joachim Mathiesen: Bernaise: A flexible framework for simulating two-phase electrohydrodynamic flows in complex domains (2018) arXiv