{
  "id": "2405.03016",
  "version": "v1",
  "published": "2024-05-05T17:51:17.000Z",
  "updated": "2024-05-05T17:51:17.000Z",
  "title": "Pathwise uniform convergence of a full discretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise",
  "authors": [
    "Binjie Li",
    "Qin Zhou"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "This paper analyzes a full discretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. The discretization uses the Euler scheme for temporal discretization and the finite element method for spatial discretization. By deriving a stability estimate of a discrete stochastic convolution and utilizing this stability estimate along with the discrete stochastic maximal $L^p$-regularity estimate, a pathwise uniform convergence rate with the general spatial $ L^q $-norms is derived.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-05T17:51:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H35",
      "35R60",
      "60H15"
    ],
    "keywords": [
      "three-dimensional stochastic allen-cahn equation",
      "full discretization",
      "multiplicative noise",
      "stability estimate",
      "discrete stochastic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}