{
  "id": "2305.06317",
  "version": "v1",
  "published": "2023-05-10T17:08:56.000Z",
  "updated": "2023-05-10T17:08:56.000Z",
  "title": "Robust Multigrid Methods for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem",
  "authors": [
    "Sijing Liu"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem and we propose multigrid methods to solve the discretized system. We prove that the $W$-cycle algorithm is uniformly convergent in the energy norm and is robust with respect to a regularization parameter on convex domains. Numerical results are shown for both $W$ -cycle and $V$-cycle algorithms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-10T17:08:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic optimal control problem",
      "robust multigrid methods",
      "discontinuous galerkin discretizations",
      "elliptic distributed optimal control problem",
      "cycle algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}