Convergence of variational approximation schemes for elastodynamics with polyconvex energy

Alexey Miroshnikov, Athanasios Tzavaras

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 Lp-theory bounds, and provides an error estimate for the approximation before the formation of shocks.

Original languageEnglish (US)
Pages (from-to)43-64
Number of pages22
JournalZeitschrift fur Analysis und ihre Anwendung
Volume33
Issue number1
DOIs
StatePublished - Feb 3 2014

Keywords

  • Nonlinear elasticity
  • Polyconvexity
  • Variational approximation scheme

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this