JournalszaaVol. 33, No. 1pp. 43–64

Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy

  • Alexey Miroshnikov

    University of Maryland, College Park, USA
  • Athanasios E. Tzavaras

    University of Crete, Heraklion, Greece
Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy cover
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Abstract

We consider a variational scheme developed by S. Demoulini, D. M. A. Stuart and A. E. Tzavaras [Arch. Ration. Mech. Anal. 157 (2001), 325–344] 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 LpL^p-theory bounds, and provides an error estimate for the approximation before the formation of shocks.

Cite this article

Alexey Miroshnikov, Athanasios E. Tzavaras, Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy. Z. Anal. Anwend. 33 (2014), no. 1, pp. 43–64

DOI 10.4171/ZAA/1498