{
  "id": "1908.09331",
  "version": "v1",
  "published": "2019-08-25T14:03:16.000Z",
  "updated": "2019-08-25T14:03:16.000Z",
  "title": "Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus",
  "authors": [
    "Ting Ma",
    "Rongchan Zhu"
  ],
  "categories": [
    "math.PR",
    "cs.NA",
    "math.AP",
    "math.NA"
  ],
  "abstract": "In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations driven by space-time white noise on $\\T$. First we prove that the convergence rate for stochastic 2D heat equation is of order $\\alpha-\\delta$ in Besov space $\\C^{-\\alpha}$ for $\\alpha\\in(0,1)$ and $\\delta>0$ arbitrarily small. Then we obtain the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations of order $\\alpha-\\delta$ in $\\C^{-\\alpha}$ for $\\alpha\\in(0,2/9)$ and $\\delta>0$ arbitrarily small.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-25T14:03:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convergence rate",
      "galerkin approximation",
      "2d torus",
      "stochastic allen-cahn equations driven",
      "stochastic 2d heat equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}