{
  "id": "2304.12816",
  "version": "v1",
  "published": "2023-04-25T13:42:43.000Z",
  "updated": "2023-04-25T13:42:43.000Z",
  "title": "Post-processing and improved error estimates of numerical methods for evolutionary systems",
  "authors": [
    "Sebastian Franz"
  ],
  "comment": "22 pages, 2 figures",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We consider evolutionary systems, i.e. systems of linear partial differential equations arising from the mathematical physics. For these systems there exists a general solution theory in exponentially weighted spaces which can be exploited in the analysis of numerical methods. The numerical method considered in this paper is a discontinuous Galerkin method in time combined with a conforming Galerkin method in space. Building on our recent paper, we improve some of the results, study the dependence of the numerical solution on the weight-parameter, consider a reformulation and post-processing of its numerical solution. As a by-product we provide error estimates for the dG-C0 method. Numerical simulations support the theoretical findings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-25T13:42:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65J08",
      "65J10",
      "65M12",
      "65M60"
    ],
    "keywords": [
      "numerical method",
      "evolutionary systems",
      "error estimates",
      "galerkin method",
      "post-processing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}