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The stability barrier of a class of Hermite-type discretizations of advection equations — arXiv:2609.33201

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.33201
License (as archived): CC0-1.0
Archived: 2026-10-07T23:25:12.689Z
SHA-256 of the archived text: 7582dbdb9d19648329231ff024f2c65641f6bd1ebc6b59931f25147377e663e5
Stable URL of this page: https://metraipolis.com/documento/dc_2c76fc0bd8da

How to cite

The stability barrier of a class of Hermite-type discretizations of advection equations — arXiv:2609.33201 — arXiv (en), https://arxiv.org/abs/2609.33201 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2c76fc0bd8da (Metraipolis archive dc_2c76fc0bd8da, sha256 7582dbdb9d19648329231ff024f2c65641f6bd1ebc6b59931f25147377e663e5)

BibTeX

@misc{dc2c76fc0bd8da,
  title = {The stability barrier of a class of Hermite-type discretizations of advection equations — arXiv:2609.33201},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.33201},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2c76fc0bd8da; sha256 7582dbdb9d19648329231ff024f2c65641f6bd1ebc6b59931f25147377e663e5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.33201. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In this paper we fully categorize all hybrid-variable (HV) discretizations of linear advection equations according to their stability property and establish the stability barrier of these methods. In the HV discretization framework, we find numerical approximations to both cell-averaged solutions and nodal solutions and evolve them in time simultaneously. We prove that the HV methods have a similar stability barrier as the classical finite difference schemes, that the semi-discretized HV scheme is stable if and only if it uses a stencil such that the number of unknowns in the upwind direction is precisely that in the downwind direction plus one or two, with only one exception when the two numbers are three and zero, respectively. It is also proved that all central HV schemes are neutrally stable, in the sense that the L2-norm of the solution remain uniformly bounded at all times. The theoretical predictions are verify by extensive numerical tests.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-29 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2609.33201 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T23:04:09.481Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).