{
  "id": "2310.01713",
  "version": "v1",
  "published": "2023-10-03T00:55:10.000Z",
  "updated": "2023-10-03T00:55:10.000Z",
  "title": "Greedy invariant-domain preserving approximation for hyperbolic systems",
  "authors": [
    "Jean-Luc Guermond",
    "Matthias Maier",
    "Bojan Popov",
    "Laura Saavedra",
    "Ignacio Tomas"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "The paper focuses on invariant-domain preserving approximations of hyperbolic systems. We propose a new way to estimate the artificial viscosity that has to be added to make explicit, conservative, consistent numerical methods invariant-domain preserving and entropy inequality compliant. Instead of computing an upper bound on the maximum wave speed in Riemann problems, we estimate a minimum wave speed in the said Riemann problems such that the approximation satisfies predefined invariant-domain properties and predefined entropy inequalities. This technique eliminates non-essential fast waves from the construction of the artificial viscosity, while preserving pre-assigned invariant-domain properties and entropy inequalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-03T00:55:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "65M60",
      "65M12",
      "65N30"
    ],
    "keywords": [
      "greedy invariant-domain preserving approximation",
      "hyperbolic systems",
      "satisfies predefined invariant-domain properties",
      "entropy inequality",
      "technique eliminates non-essential fast waves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}