{
  "id": "2003.08504",
  "version": "v1",
  "published": "2020-03-18T23:27:50.000Z",
  "updated": "2020-03-18T23:27:50.000Z",
  "title": "A One Dimensional Elliptic Distributed Optimal Control Problem with Pointwise Derivative Constraints",
  "authors": [
    "Susanne C. Brenner",
    "Li-yeng Sung",
    "Winnifried Wollner"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain higher regularity for the optimal state under appropriate assumptions on the data. We also solve the optimal control problem as a fourth order variational inequality by a $C^1$ finite element method, and present the error analysis together with numerical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-18T23:27:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic distributed optimal control problem",
      "dimensional elliptic distributed optimal control",
      "pointwise derivative constraints",
      "optimal state",
      "fourth order variational inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}