{
  "id": "1404.6030",
  "version": "v3",
  "published": "2014-04-24T05:37:22.000Z",
  "updated": "2016-01-25T20:41:47.000Z",
  "title": "On the convergence of a shock capturing discontinuous Galerkin method for nonlinear hyperbolic systems of conservation laws",
  "authors": [
    "Mohammad Zakerzadeh",
    "Georg May"
  ],
  "comment": "Comments: Affiliations added Comments: Numerical results added, shortened proof",
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper, we present a shock capturing discontinuous Galerkin (SC-DG) method for nonlinear systems of conservation laws in several space dimensions and analyze its stability and convergence. The scheme is realized as a space-time formulation in terms of entropy variables using an entropy stable numerical flux. While being similar to the method proposed in [14], our approach is new in that we do not use streamline diffusion (SD) stabilization. It is proved that an artificial-viscosity-based nonlinear shock capturing mechanism is sufficient to ensure both entropy stability and entropy consistency, and consequently we establish convergence to an entropy measure-valued (emv) solution. The result is valid for general systems and arbitrary order discontinuous Galerkin method.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-25T08:27:04.000Z",
      "comment": "Comments: Affiliations added",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-01-25T20:41:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "65M60",
      "65M12"
    ],
    "keywords": [
      "shock capturing discontinuous galerkin method",
      "nonlinear hyperbolic systems",
      "conservation laws",
      "nonlinear shock capturing mechanism",
      "order discontinuous galerkin method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.6030Z"
    }
  }
}