{
  "id": "1411.1944",
  "version": "v1",
  "published": "2014-11-07T15:18:08.000Z",
  "updated": "2014-11-07T15:18:08.000Z",
  "title": "A Multiscale Method for Porous Microstructures",
  "authors": [
    "Donald L. Brown",
    "Daniel Peterseim"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper we develop a multiscale method to solve problems in complicated porous microstructures with Neumann boundary conditions. By using a coarse-grid quasi-interpolation operator to define a fine detail space and local orthogonal decomposition, we construct multiscale corrections to coarse-grid basis functions with microstructure. By truncating the corrector functions we are able to make a computationally efficient scheme. Error results and analysis are presented. A key component of this analysis is the investigation of the Poincar\\'{e} constants in perforated domains as they may contain micro-structural information. Using a constructive method originally developed for weighted Poincar\\'{e} inequalities, we are able to obtain estimates on Poincar\\'{e} constants with respect to scale and separation length of the pores. Finally, two numerical examples are presented to verify our estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-07T15:18:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiscale method",
      "porous microstructures",
      "local orthogonal decomposition",
      "contain micro-structural information",
      "coarse-grid basis functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.1944B"
    }
  }
}