Eto, Tokuhiro and Garcke, Harald and Nuernberg, Robert (2024) A structure-preserving finite element method for the multi-phase Mullins-Sekerka problem with triple junctions. NUMERISCHE MATHEMATIK, 156 (4). pp. 1479-1509. ISSN 0029-599X, 0945-3245
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We consider a sharp interface formulation for the multi-phase Mullins-Sekerka flow. The flow is characterized by a network of curves evolving such that the total surface energy of the curves is reduced, while the areas of the enclosed phases are conserved. Making use of a variational formulation, we introduce a fully discrete finite element method. Our discretization features a parametric approximation of the moving interfaces that is independent of the discretization used for the equations in the bulk. The scheme can be shown to be unconditionally stable and to satisfy an exact volume conservation property. Moreover, an inherent tangential velocity for the vertices on the discrete curves leads to asymptotically equidistributed vertices, meaning no remeshing is necessary in practice. Several numerical examples, including a convergence experiment for the three-phase Mullins-Sekerka flow, demonstrate the capabilities of the introduced method.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAHN-HILLIARD EQUATION; IMPLICIT TIME DISCRETIZATION; NUMERICAL-ANALYSIS; GRADIENT FLOWS; APPROXIMATION; EXISTENCE; SURFACE; 35K55; 35R35; 65M12; 65M50; 65M60; 74E10; 74E15; 80A22 |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Sep 2025 09:22 |
| Last Modified: | 15 Sep 2025 09:22 |
| URI: | https://pred.uni-regensburg.de/id/eprint/64111 |
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