{
  "id": "1907.03852",
  "version": "v1",
  "published": "2019-07-08T20:23:05.000Z",
  "updated": "2019-07-08T20:23:05.000Z",
  "title": "Quasi-optimal adaptive mixed finite element methods for controlling natural norm errors",
  "authors": [
    "Yuwen Li"
  ],
  "comment": "24 pages",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "For a generalized Hodge--Laplace equation, we prove the quasi-optimal convergence rate of an adaptive mixed finite element method controlling the error in the natural mixed variational norm. In particular, we obtain new quasi-optimal adaptive mixed methods for the scalar Poisson, vector Poisson, and Stokes equations. Comparing to existing adaptive mixed methods, the new methods control errors in both two variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-08T20:23:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N12",
      "65N15",
      "65N30",
      "65N50",
      "41A25"
    ],
    "keywords": [
      "adaptive mixed finite element method",
      "quasi-optimal adaptive mixed finite element",
      "controlling natural norm errors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}