{
  "id": "1408.0820",
  "version": "v1",
  "published": "2014-08-04T21:14:46.000Z",
  "updated": "2014-08-04T21:14:46.000Z",
  "title": "Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy",
  "authors": [
    "Alexey Miroshnikov",
    "Athanasios E. Tzavaras"
  ],
  "journal": "Journal of Analysis and Its Applications (ZAA), 33 (2014), 43-64",
  "doi": "10.4171/ZAA/1498",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a variational scheme developed by S. Demoulini, D. M. A. Stuart and A. E. Tzavaras [Arch. Ration. Mech. Anal. 157 (2001)] that approximates the equations of three dimensional elastodynamics with polyconvex stored energy. We establish the convergence of the time-continuous interpolates constructed in the scheme to a solution of polyconvex elastodynamics before shock formation. The proof is based on a relative entropy estimation for the time-discrete approximants in an environment of Lp-theory bounds, and provides an error estimate for the approximation before the formation of shocks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-04T21:14:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L70",
      "74B20",
      "74H20"
    ],
    "keywords": [
      "variational approximation schemes",
      "polyconvex energy",
      "convergence",
      "error estimate",
      "polyconvex stored energy"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.0820M"
    }
  }
}