{
  "id": "1801.03548",
  "version": "v1",
  "published": "2018-01-10T20:38:10.000Z",
  "updated": "2018-01-10T20:38:10.000Z",
  "title": "On strong $L^2$ convergence of numerical schemes for the stochastic 2D Navier-Stokes equations",
  "authors": [
    "Hakima Bessaih",
    "Annie Millet"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that some discretization schemes for the 2D Navier-Stokes equations subject to a random perturbation converge in $L^2(\\Omega)$. This refines previous results which only established the convergence in probability of these numerical approximations. Using exponential moment estimates of the solution of the stochastic NS equations and convergence of a localized scheme, we can prove strong convergence of fully implicit and semi-implicit time Euler discretizations, and of a splitting scheme. The speed of the $L^2(\\Omega)$-convergence depends on the diffusion coefficient and on the viscosity parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-10T20:38:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H35",
      "76D06",
      "76M35"
    ],
    "keywords": [
      "stochastic 2d navier-stokes equations",
      "convergence",
      "numerical schemes",
      "semi-implicit time euler discretizations",
      "2d navier-stokes equations subject"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}