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A Lloyd-stabilized Voronoï 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(h1/4). 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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Cite

BibTeXRIS
BibTeX
@misc{despres2026lloydstabilized,
  title = {{A Lloyd-stabilized Voronoï particle method}},
  author = {Bruno Després and Borjan Geshkovski},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28135},
  eprint = {2609.28135},
  archivePrefix = {arXiv},
  url = {https://inria.hal.science/hal-05762240v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Lloyd-stabilized Voronoï particle method
AU  - Bruno Després
AU  - Borjan Geshkovski
PY  - 2026
DA  - 2026/09/23
PB  - HAL
DO  - 10.48550/arxiv.2609.28135
UR  - https://inria.hal.science/hal-05762240v1
AB  - 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.
ER  -