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PreprintCC BY 4.0HAL

Finite volume discretization and normalized gradient flow for computing minimizers of the rotating Gross-Pitaevskii energy

  • Quentin Chauleur
  • Guillaume Dujardin
  • Robin Roussel
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Abstract

We study the approximation by a finite volume scheme of the stationary Gross-Pitaevskii equation with angular momentum rotation. We prove that, under standard mesh regularity assumptions, the discrete global minimizers converge to the continuous one as the mesh diameter tends to zero. Moreover, under a spectral gap assumption on the Hessian of the discrete energy, we prove that solutions to a normalized continuous gradient flow converges exponentially fast to such discrete minimizers. Additionally, we show that this previous discrete spectral gap assumption can be derived from similar hypotheses in the continuous setting. We support our theoretical results with numerical simulations, which broaden the scope of the analysis.

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Cite

BibTeXRIS
BibTeX
@misc{chauleur2026finite,
  title = {{Finite volume discretization and normalized gradient flow for computing minimizers of the rotating Gross-Pitaevskii energy}},
  author = {Quentin Chauleur and Guillaume Dujardin and Robin Roussel},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11820},
  eprint = {2610.11820},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05785848v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Finite volume discretization and normalized gradient flow for computing minimizers of the rotating Gross-Pitaevskii energy
AU  - Quentin Chauleur
AU  - Guillaume Dujardin
AU  - Robin Roussel
PY  - 2026
DA  - 2026/10/08
PB  - HAL
DO  - 10.48550/arxiv.2610.11820
UR  - https://hal.science/hal-05785848v1
AB  - We study the approximation by a finite volume scheme of the stationary Gross-Pitaevskii equation with angular momentum rotation. We prove that, under standard mesh regularity assumptions, the discrete global minimizers converge to the continuous one as the mesh diameter tends to zero. Moreover, under a spectral gap assumption on the Hessian of the discrete energy, we prove that solutions to a normalized continuous gradient flow converges exponentially fast to such discrete minimizers. Additionally, we show that this previous discrete spectral gap assumption can be derived from similar hypotheses in the continuous setting. We support our theoretical results with numerical simulations, which broaden the scope of the analysis.
ER  -