{
  "id": "1604.05120",
  "version": "v1",
  "published": "2016-04-18T12:43:35.000Z",
  "updated": "2016-04-18T12:43:35.000Z",
  "title": "Error estimates in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems",
  "authors": [
    "Hans-Goerg Roos"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "Error estimates of finite element methods for reaction-diffusion Problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the $H^1$ seminorm leads to a balanced norm which reflects the layer behavior correctly. We discuss also anisotropic problems, semilinear equations, supercloseness and a combination technique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-18T12:43:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite element methods",
      "error estimates",
      "reaction-diffusion problems",
      "balanced norm",
      "shishkin meshes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}