A convergent finite element method for two-phase Stokes flow driven by surface tension
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908556737904640 |
|---|---|
| author | Bai, Genming Garcke, Harald Veerapaneni, Shravan |
| author_facet | Bai, Genming Garcke, Harald Veerapaneni, Shravan |
| contents | We present the first convergence proof for an iso-parametric finite element discretization of two-phase Stokes flow in $Ω\subset \mathbb{R}^d$, $d=2,3$, with interface dynamics governed by mean curvature. The proof relies on a crucial discrete coupled parabolicity structure of the error system and a powerful iso-parametric framework of convergence analysis where we do not really discriminate consistency and stability. This new mixing idea leads to a non-trivial construction of the bulk mesh in the consistency analysis. The techniques and analysis developed in this paper provide fundamental numerical analysis tools for general curvature-driven free boundary problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20111 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A convergent finite element method for two-phase Stokes flow driven by surface tension Bai, Genming Garcke, Harald Veerapaneni, Shravan Numerical Analysis We present the first convergence proof for an iso-parametric finite element discretization of two-phase Stokes flow in $Ω\subset \mathbb{R}^d$, $d=2,3$, with interface dynamics governed by mean curvature. The proof relies on a crucial discrete coupled parabolicity structure of the error system and a powerful iso-parametric framework of convergence analysis where we do not really discriminate consistency and stability. This new mixing idea leads to a non-trivial construction of the bulk mesh in the consistency analysis. The techniques and analysis developed in this paper provide fundamental numerical analysis tools for general curvature-driven free boundary problems. |
| title | A convergent finite element method for two-phase Stokes flow driven by surface tension |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2509.20111 |