{
  "id": "1509.08384",
  "version": "v1",
  "published": "2015-09-28T16:33:23.000Z",
  "updated": "2015-09-28T16:33:23.000Z",
  "title": "A multiscale finite element method for oscillating Neumann problem on rough domain",
  "authors": [
    "P. B. Ming",
    "X. Xu"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We develop a new multiscale finite element method for Laplace equation with oscillating Neumann boundary conditions on rough boundaries. The key point is the introduction of a new boundary condition that incorporates both the microscopically geometrical and physical information of the rough boundary. We prove the method has optimal convergence rate in the energy norm with a weak resonance term for periodic roughness. Numerical results are reported for both periodic and nonperiodic roughness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-28T16:33:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiscale finite element method",
      "oscillating neumann problem",
      "rough domain",
      "rough boundary",
      "oscillating neumann boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}