{
  "id": "1002.3793",
  "version": "v1",
  "published": "2010-02-19T17:45:50.000Z",
  "updated": "2010-02-19T17:45:50.000Z",
  "title": "Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission condition",
  "authors": [
    "Adrian Muntean",
    "Omar Lakkis"
  ],
  "comment": "14 pages, table of contents",
  "categories": [
    "math.NA",
    "math.AP"
  ],
  "abstract": "We study a two-scale reaction-diffusion system with nonlinear reaction terms and a nonlinear transmission condition (remotely ressembling Henry's law) posed at air-liquid interfaces. We prove the rate of convergence of the two-scale Galerkin method proposed in Muntean & Neuss-Radu (2009) for approximating this system in the case when both the microstructure and macroscopic domain are two-dimensional. The main difficulty is created by the presence of a boundary nonlinear term entering the transmission condition. Besides using the particular two-scale structure of the system, the ingredients of the proof include two-scale interpolation-error estimates, an interpolation-trace inequality, and improved regularity estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-19T17:45:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M60",
      "65M15",
      "35K57",
      "65L70",
      "80A32",
      "35B27"
    ],
    "keywords": [
      "two-scale reaction-diffusion system",
      "nonlinear transmission condition",
      "galerkin scheme approximating",
      "convergence",
      "two-scale interpolation-error estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.3793M"
    }
  }
}