{
  "id": "1411.4191",
  "version": "v1",
  "published": "2014-11-15T22:01:20.000Z",
  "updated": "2014-11-15T22:01:20.000Z",
  "title": "Finite element error estimates for an optimal control problem governed by the Burgers equation",
  "authors": [
    "Pedro Martín Merino Rosero"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation of the state and the control is done by using piecewise linear functions. With this choice, an $L^2$ superlinear order of convergence for the control is obtained; moreover, under a further assumption on the regularity structure of the optimal control this error estimate can be improved to $h^{3/2}$. The theoretical findings are tested experimentally by means of numerical examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-15T22:01:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal control problem",
      "finite element error estimates",
      "steady one-dimensional burgers equation",
      "derive a-priori error estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.4191M"
    }
  }
}