{
  "id": "2408.16511",
  "version": "v1",
  "published": "2024-08-29T13:16:48.000Z",
  "updated": "2024-08-29T13:16:48.000Z",
  "title": "On the stability of finite-volume schemes on non-uniform meshes",
  "authors": [
    "Pavel Bakhvalov",
    "Mikhail Surnachev"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper, we study the L2 stability of high-order finite-volume schemes for the 1D transport equation on non-uniform meshes. We consider the case when a small periodic perturbation is applied to a uniform mesh. For this case, we establish a sufficient stability condition. This allows to prove the (p+1)-th order convergence of finite-volume schemes based on p-th order polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-29T13:16:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M12"
    ],
    "keywords": [
      "non-uniform meshes",
      "p-th order polynomials",
      "1d transport equation",
      "sufficient stability condition",
      "small periodic perturbation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}