Eto, Tokuhiro and Garcke, Harald and Nürnberg, Robert (2026) A Parametric Finite Element Method for a Degenerate Multi-Phase Stefan Problem with Triple Junctions. COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 26 (1). pp. 43-67. ISSN 1609-4840, 1609-9389
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In this study, we propose a parametric finite element method for a degenerate multi-phase Stefan problem with triple junctions. This model describes the energy-driven motion of a surface cluster whose distributional solution was studied by Garcke and Sturzenhecker. We approximate the weak formulation of this sharp interface model by an unfitted finite element method that uses parametric elements for the representation of the moving interfaces. We establish existence and uniqueness of the discrete solution and prove unconditional stability of the proposed scheme. Moreover, a modification of the original scheme leads to a structure-preserving variant, in that it conserves the discrete analogue of a quantity that is preserved by the classical solution. Some numerical results demonstrate the applicability of our introduced schemes.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAHN-HILLIARD EQUATION; IMPLICIT TIME DISCRETIZATION; NUMERICAL-ANALYSIS; GRADIENT FLOWS; APPROXIMATION; SURFACE; EXISTENCE; SYSTEM; Degenerate Stefan Problem; Parametric Finite Element Method; Unconditional Stability; Energy Content Preservation; Multi-Phase Diffusion |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 May 2026 07:59 |
| Last Modified: | 06 May 2026 07:59 |
| URI: | https://pred.uni-regensburg.de/id/eprint/67215 |
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