{
  "id": "2401.09834",
  "version": "v1",
  "published": "2024-01-18T09:50:59.000Z",
  "updated": "2024-01-18T09:50:59.000Z",
  "title": "Convergence of a spatial semidiscretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise",
  "authors": [
    "Binjie Li",
    "Qin Zhou"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "math.PR"
  ],
  "abstract": "This paper studies the convergence of a spatial semidiscretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. For non-smooth initial values, the regularity of the mild solution is investigated, and an error estimate is derived with the spatial $ L^2 $-norm. For smooth initial values, two error estimates with the general spatial $ L^q $-norms are established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-18T09:50:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M60",
      "60H15",
      "60H35"
    ],
    "keywords": [
      "three-dimensional stochastic allen-cahn equation",
      "spatial semidiscretization",
      "multiplicative noise",
      "convergence",
      "error estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}