{
  "id": "1210.2076",
  "version": "v1",
  "published": "2012-10-07T17:03:45.000Z",
  "updated": "2012-10-07T17:03:45.000Z",
  "title": "A priori and a posteriori $W^{1,\\infty}$ error analysis of a QC method for complex lattices",
  "authors": [
    "Assyr Abdulle",
    "Ping Lin",
    "Alexander V. Shapeev"
  ],
  "comment": "23 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper we prove a priori and a posteriori error estimates for a multiscale numerical method for computing equilibria of multilattices under an external force. The error estimates are derived in a $W^{1,\\infty}$ norm in one space dimension. One of the features of our analysis is that we establish an equivalent way of formulating the coarse-grained problem which greatly simplifies derivation of the error bounds (both, a priori and a posteriori). We illustrate our error estimates with numerical experiments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-07T17:03:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "70C20",
      "74G15"
    ],
    "keywords": [
      "qc method",
      "error analysis",
      "complex lattices",
      "posteriori error estimates",
      "multiscale numerical method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.2076A"
    }
  }
}