{
  "id": "2204.13924",
  "version": "v1",
  "published": "2022-04-29T07:49:34.000Z",
  "updated": "2022-04-29T07:49:34.000Z",
  "title": "Numerical approximation of the stochastic Navier-Stokes equations through artificial compressibility",
  "authors": [
    "Jad Doghman"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "physics.class-ph"
  ],
  "abstract": "A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter $\\epsilon$. Space and time are discretized through a finite element approximation and an Euler method. The convergence analysis of the suggested numerical scheme is investigated throughout this paper. It is based on a local monotonicity property permitting the convergence toward the unique strong solution of the Navier-Stokes equations to occur within the originally introduced probability space. Justified optimal conditions are imposed on the parameter $\\epsilon$ to ensure convergence within the best rate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-29T07:49:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "numerical approximation",
      "artificial compressibility",
      "two-dimensional unsteady stochastic navier-stokes equations",
      "unique strong solution",
      "finite element approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}