{
  "id": "1811.11143",
  "version": "v1",
  "published": "2018-11-27T18:09:16.000Z",
  "updated": "2018-11-27T18:09:16.000Z",
  "title": "Some convergence and optimality results of adaptive mixed methods in finite element exterior calculus",
  "authors": [
    "Yuwen Li"
  ],
  "comment": "23 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper, we present several new a posteriori error estimators for decoupled errors and two adaptive mixed finite element methods \\textsf{AMFEM1} and \\textsf{AMFEM2} for the Hodge Laplacian problem in finite element exterior calculus. We prove that \\textsf{AMFEM1} and \\textsf{AMFEM2} are both convergent starting from any initial coarse mesh. A suitably defined quasi error is crucial to the convergence analysis. In addition, we prove the optimality of \\textsf{AMFEM2}. The main technical contribution is a localized discrete upper bound. Comparing to existing literature, our results work on Lipschitz domains with nontrivial cohomology and provide the first norm convergence and optimality results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-27T18:09:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N15"
    ],
    "keywords": [
      "finite element exterior calculus",
      "adaptive mixed methods",
      "optimality results",
      "mixed finite element methods",
      "posteriori error estimators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}