{
  "id": "2207.10853",
  "version": "v1",
  "published": "2022-07-22T03:04:00.000Z",
  "updated": "2022-07-22T03:04:00.000Z",
  "title": "Error Estimate of Multiscale Finite Element Method for Periodic Media Revisited",
  "authors": [
    "Pingbing Ming",
    "Siqi Song"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We derive the optimal energy error estimate for multiscale finite element method with oversampling technique applying to elliptic system with rapidly oscillating periodic coefficients under the assumption that the coefficients are bounded and measurable, which may admit rough microstructures. As a by-product of the energy estimate, we derive the rate of convergence in L$^{d/(d-1)}-$norm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-22T03:04:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiscale finite element method",
      "periodic media",
      "optimal energy error estimate",
      "admit rough microstructures",
      "energy estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}