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arXiv · 2609.28135

A Lloyd-stabilized Voronoi particle method

Bruno Després·Borjan Geshkovski
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Abstract

We study the stability and consistency of Lloyd's algorithm used in combination with the Lagrangian transport of a density on a Voronoï tessellation. We show that relaxation rates as strong as $O(h^{-1/2})$, where $h$ is the mesh size, give convergence to the continuity equation in Wasserstein distance at the rate $O(h^{1/4})$. Thus the mesh can be kept regular by the correction alone, without the remeshing that Lagrangian methods usually require. An application is proposed for the compressible Euler equations.

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Bruno Després, Borjan Geshkovski. 2026-09-23. A Lloyd-stabilized Voronoi particle method. https://arxiv.org/abs/2609.28135

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