Metzger S (2021)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2021
Book Volume: 59
Pages Range: 219-248
Journal Issue: 1
DOI: 10.1137/19M1280740
The Cahn--Hilliard equation is a widely used model that describes among othersphase-separation processes of binary mixtures or two-phase flows. In recent years, different types ofboundary 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 additionalCahn--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 mappingbetween the phase-field parameter and the chemical potential inside of the domain, we are able topostulate an efficient, unconditionally energy stable finite element scheme. Furthermore, we establishthe convergence of discrete solutions toward suitable weak solutions of the original model. This servesalso as an additional pathway to establish existence of weak solutions. Furthermore, we presentsimulations underlining the practicality of the proposed scheme and investigate its experimentalorder of convergence.
APA:
Metzger, S. (2021). An Efficient and Convergent Finite Element Scheme for Cahn-Hilliard Equations with Dynamic Boundary Conditions. SIAM Journal on Numerical Analysis, 59(1), 219-248. https://dx.doi.org/10.1137/19M1280740
MLA:
Metzger, Stefan. "An Efficient and Convergent Finite Element Scheme for Cahn-Hilliard Equations with Dynamic Boundary Conditions." SIAM Journal on Numerical Analysis 59.1 (2021): 219-248.
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