Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy
Analysis of PDEs
2014-08-06 v1
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.
Cite
@article{arxiv.1408.0820,
title = {Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy},
author = {Alexey Miroshnikov and Athanasios E. Tzavaras},
journal= {arXiv preprint arXiv:1408.0820},
year = {2014}
}