{
  "id": "2110.10611",
  "version": "v1",
  "published": "2021-10-20T15:12:17.000Z",
  "updated": "2021-10-20T15:12:17.000Z",
  "title": "Analysis of pressure-robust embedded-hybridized discontinuous Galerkin methods for the Stokes problem under minimal regularity",
  "authors": [
    "Aaron Baier-Reinio",
    "Sander Rhebergen",
    "Garth N. Wells"
  ],
  "doi": "10.1007/s10915-022-01889-6",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We present analysis of two lowest-order hybridizable discontinuous Galerkin methods for the Stokes problem, while making only minimal regularity assumptions on the exact solution. The methods under consideration have previously been shown to produce $H(\\textrm{div})$-conforming and divergence-free approximate velocities. Using these properties, we derive a priori error estimates for the velocity that are independent of the pressure. These error estimates, which assume only $H^{1+s}$-regularity of the exact velocity fields for any $s \\in [0, 1]$, are optimal in a discrete energy norm. Error estimates for the velocity and pressure in the $L^2$-norm are also derived in this minimal regularity setting. Our theoretical findings are supported by numerical computations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-10-20T15:12:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N12",
      "65N15",
      "65N30",
      "76D07"
    ],
    "keywords": [
      "pressure-robust embedded-hybridized discontinuous galerkin methods",
      "minimal regularity",
      "stokes problem",
      "error estimates",
      "hybridizable discontinuous galerkin methods"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}