Knopf, Patrik and Lam, Kei Fong and Liu, Chun and Metzger, Stefan (2021) Phase-field dynamics with transfer of materials: The Cahn-Hillard equation with reaction rate dependent dynamic boundary conditions. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 55 (1). pp. 229-282. ISSN 0764-583X, 1290-3841
Full text not available from this repository. (Request a copy)Abstract
The Cahn-Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic boundary conditions for the Cahn-Hilliard equation have been proposed and investigated in recent times. Of particular interests are the model by Goldstein et al. [Phys. D 240 (2011) 754-766] and the model by Liu and Wu [Arch. Ration. Mech. Anal. 233 (2019) 167-247]. Both of these models satisfy similar physical properties but differ greatly in their mass conservation behaviour. In this paper we introduce a new model which interpolates between these previous models, and investigate analytical properties such as the existence of unique solutions and convergence to the previous models mentioned above in both the weak and the strong sense. For the strong convergences we also establish rates in terms of the interpolation parameter, which are supported by numerical simulations obtained from a fully discrete, unconditionally stable and convergent finite element scheme for the new interpolation model.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Cahn&-Hilliard equation; dynamic boundary conditions; relaxation by Robin boundary conditions; gradient flow; finite element analysis |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 18 Aug 2022 05:31 |
| Last Modified: | 18 Aug 2022 05:31 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46704 |
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