{
  "id": "1402.6402",
  "version": "v1",
  "published": "2014-02-26T03:44:14.000Z",
  "updated": "2014-02-26T03:44:14.000Z",
  "title": "Model reduction and mesh refinement",
  "authors": [
    "Panagiotis Stinis"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "In recent work we have presented a novel algorithm for mesh refinement which utilizes a reduced model. In particular, the reduced model is used to monitor the transfer of activity (e.g. mass, energy) from larger to smaller scales. When the activity transfer rate exceeds a prescribed tolerance, the algorithm refines the mesh accordingly. The algorithm was applied to the inviscid Burgers and focusing Schr\\\"odinger equations to detect singularities. We offer here a simple proof of why the use of a reduced model for mesh refinement is a good idea. We do so by showing that by controlling the transfer of activity rate one controls the error caused inevitably by a finite resolution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-26T03:44:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M50",
      "35L67",
      "76B99",
      "65M70"
    ],
    "keywords": [
      "mesh refinement",
      "model reduction",
      "reduced model",
      "activity transfer rate exceeds",
      "algorithm refines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.6402S"
    }
  }
}