| Issue |
ESAIM: M2AN
Volume 59, Number 1, January-February 2025
|
|
|---|---|---|
| Page(s) | 419 - 448 | |
| DOI | https://doi.org/10.1051/m2an/2024005 | |
| Published online | 08 January 2025 | |
Implicit like time discretization for the one-phase Hele-Shaw problem with surface tension
1
Departament de Física de la Matèria Condensada, Universitat de Barcelona, Avinguda Diagonal 647, 08028 Barcelona, Spain
2
LaMME, UMR CNRS 8071, Université Évry Val d’Essonne, Évry-Courcouronnes, France
3
Laboratoire Jean Alexandre Dieudonné, UMR CNRS 7351, Université de Nice, Nice, France
* Corresponding author: nicolas.meunier@univ-evry.fr
Received:
10
May
2023
Accepted:
11
January
2024
In this work, we propose and compare different numerical methods to handle the one-phase Hele-Shaw problem with surface tension in dimension two by using three variational approaches in the spirit of the seminal works [F. Otto, Arch. Ration. Mech. Anal. 141 (1998) 63–103.], [L. Giacomelli and F. Otto, Calc. Var. Partial Differ. Equ. 13 (2001) 377–403.].
Mathematics Subject Classification: 49M15 / 49M25 / 76D27
Key words: Existence of minimizer / gradient descent method
© The authors. Published by EDP Sciences, SMAI 2025
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