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arXiv · 2509.20111

A convergent finite element method for two-phase Stokes flow driven by surface tension

Genming Bai·Harald Garcke·Shravan Veerapaneni
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Abstract

We present the first convergence proof for an iso-parametric finite element discretization of two-phase Stokes flow in $\Omega \subset \mathbb{R}^d$, $d=2,3$, 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.

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Genming Bai, Harald Garcke, Shravan Veerapaneni. 2025-09-24. A convergent finite element method for two-phase Stokes flow driven by surface tension. https://arxiv.org/abs/2509.20111

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