{
  "id": "1003.3641",
  "version": "v2",
  "published": "2010-03-18T17:36:06.000Z",
  "updated": "2012-11-28T23:41:27.000Z",
  "title": "A posteriori $L^\\infty(L^2)$-error bounds in finite element approximation of the wave equation",
  "authors": [
    "Emmanuil H. Georgoulis",
    "Omar Lakkis",
    "Charalambos Makridakis"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We address the error control of Galerkin discretization (in space) of linear second order hyperbolic problems. More specifically, we derive a posteriori error bounds in the L\\infty(L2)-norm for finite element methods for the linear wave equation, under minimal regularity assumptions. The theory is developed for both the space-discrete case, as well as for an implicit fully discrete scheme. The derivation of these bounds relies crucially on carefully constructed space- and time-reconstructions of the discrete numerical solutions, in conjunction with a technique introduced by Baker (1976, SIAM J. Numer. Anal., 13) in the context of a priori error analysis of Galerkin discretization of the wave problem in weaker-than-energy spatial norms.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-28T23:41:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M60",
      "65M15"
    ],
    "keywords": [
      "finite element approximation",
      "wave equation",
      "error bounds",
      "posteriori",
      "linear second order hyperbolic problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.3641G"
    }
  }
}