{
  "id": "2301.10639",
  "version": "v1",
  "published": "2023-01-25T15:22:07.000Z",
  "updated": "2023-01-25T15:22:07.000Z",
  "title": "Low regularity error estimates for the time integration of 2D NLS",
  "authors": [
    "Lun Ji",
    "Alexander Ostermann",
    "Frédéric Rousset",
    "Katharina Schratz"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "A filtered Lie splitting scheme is proposed for the time integration of the cubic nonlinear Schr\\\"odinger equation on the two-dimensional torus $\\mathbb{T}^2$. The scheme is analyzed in a framework of discrete Bourgain spaces, which allows us to consider initial data with low regularity; more precisely initial data in $H^s(\\mathbb{T}^2)$ with $s>0$. In this way, the usual stability restriction to smooth Sobolev spaces with index $s>1$ is overcome. Rates of convergence of order $\\tau^{s/2}$ in $L^2(\\mathbb{T}^2)$ at this regularity level are proved. Numerical examples illustrate that these convergence results are sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-25T15:22:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M12",
      "65M15",
      "35Q55"
    ],
    "keywords": [
      "low regularity error estimates",
      "time integration",
      "2d nls",
      "initial data",
      "smooth sobolev spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}