{
  "id": "2304.13839",
  "version": "v1",
  "published": "2023-04-26T21:53:35.000Z",
  "updated": "2023-04-26T21:53:35.000Z",
  "title": "$L^2(I;H^1(Ω))$ and $L^2(I;L^2(Ω))$ best approximation type error estimates for Galerkin solutions of transient Stokes problems",
  "authors": [
    "Dmitriy Leykekhman",
    "Boris Vexler"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2107.11051",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper we establish best approximation type estimates for the fully discrete Galerkin solutions of transient Stokes problem in $L^2(I;L^2(\\Omega)^d)$ and $L^2(I;H^1(\\Omega)^d)$ norms. These estimates fill the gap in the error analysis of the transient Stokes problems and have a number of applications. The analysis naturally extends to inhomogeneous parabolic problems. The best type $L^2(I;H^1(\\Omega))$ error estimates seems to be new even for scalar parabolic problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-26T21:53:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30"
    ],
    "keywords": [
      "best approximation type error estimates",
      "transient stokes problem",
      "galerkin solutions",
      "best approximation type estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}