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

2025/09/24 by Genming Bai, Harald Garcke, Bai, Genming +3 · 1 citation
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paper · pdf · doi:10.48550/arxiv.2509.20111

Abstract

We present the first convergence proof for an iso-parametric finite element discretization of two-phase Stokes flow in Ω⊂ 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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