{
  "id": "1710.03471",
  "version": "v1",
  "published": "2017-10-10T09:30:57.000Z",
  "updated": "2017-10-10T09:30:57.000Z",
  "title": "Convergence analysis of finite element approximation of large deviation principle",
  "authors": [
    "Xiaoliang Wan",
    "Haijun Yu",
    "Jiayu Zhai"
  ],
  "comment": "24 pages, 5 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "In this work, we address the convergence of the finite element approximation of the minimizer of the Freidlin-Wentzell (F-W) action functional for a non-gradient dynamical system perturbed by small noise. The F-W theory of large deviations is a rigorous mathematical tool to study small-noise-induced transitions in a dynamical system. The central task in the application of F-W theory of large deviations is to seek the minimizer and minimum of the F-W action functional. We discretize the F-W action functional using linear finite element, and establish the convergence of the approximate minimizer through $\\Gamma$-convergence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-10T09:30:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M60",
      "65P40",
      "65K10"
    ],
    "keywords": [
      "finite element approximation",
      "large deviation principle",
      "convergence analysis",
      "f-w action functional",
      "f-w theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}