{
  "id": "1710.08289",
  "version": "v1",
  "published": "2017-10-20T10:39:00.000Z",
  "updated": "2017-10-20T10:39:00.000Z",
  "title": "Optimal adaptivity for a standard finite element method for the Stokes problem",
  "authors": [
    "Michael Feischl"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1710.06082",
  "categories": [
    "math.NA"
  ],
  "abstract": "We prove that the a standard adaptive algorithm for the Taylor-Hood discretization of the stationary Stokes problem converges with optimal rate. This is done by developing an abstract framework for indefinite problems which allows us to prove general quasi-orthogonality proposed in [Carstensen et al., 2014]. This property is the main obstacle towards the optimality proof and therefore is the main focus of this work. The key ingredient is a new connection between the mentioned quasi-orthogonality and $LU$-factorizations of infinite matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-20T10:39:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "standard finite element method",
      "optimal adaptivity",
      "stationary stokes problem converges",
      "infinite matrices",
      "standard adaptive algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}