{
  "id": "2305.01340",
  "version": "v1",
  "published": "2023-05-02T11:38:42.000Z",
  "updated": "2023-05-02T11:38:42.000Z",
  "title": "A-posteriori error estimates for systems of hyperbolic conservation laws",
  "authors": [
    "Jan Giesselmann",
    "Aleksey Sikstel"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We provide rigorous and computable a-posteriori error estimates for first order finite-volume approximations of nonlinear systems of hyperbolic conservation laws in one spatial dimension. Our estimators rely on recent stability results by Bressan, Chiri and Shen and a novel method to compute negative order norms of residuals. Numerical experiments show that the error estimator converges with the rate predicted by a-priori error estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-02T11:38:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L40",
      "65M08",
      "65M15"
    ],
    "keywords": [
      "hyperbolic conservation laws",
      "first order finite-volume approximations",
      "a-priori error estimates",
      "computable a-posteriori error estimates",
      "error estimator converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}