{
  "id": "1908.08981",
  "version": "v1",
  "published": "2019-08-23T19:07:24.000Z",
  "updated": "2019-08-23T19:07:24.000Z",
  "title": "Ultraweak formulation of linear PDEs in nondivergence form and DPG approximation",
  "authors": [
    "Thomas Führer"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We develop and analyze an ultraweak formulation of linear PDEs in nondivergence form where the coefficients satisfy the Cordes condition. Based on the ultraweak formulation we propose discontinuous Petrov--Galerkin (DPG) methods. We investigate Fortin operators for the fully discrete schemes and provide a posteriori estimators for the methods under consideration. Numerical experiments are presented in the case of uniform and adaptive mesh-refinement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-23T19:07:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N12"
    ],
    "keywords": [
      "ultraweak formulation",
      "linear pdes",
      "nondivergence form",
      "dpg approximation",
      "cordes condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}