Alexey Miroshnikov, Athanasios E. Tzavaras
Published 2014-08-04Version 1
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.
Journal: Journal of Analysis and Its Applications (ZAA), 33 (2014), 43-64
On the convergence of statistical solutions of the 3D Navier-Stokes-$α$ model as $α$ vanishes
Error estimate for the Finite Volume Scheme applied to the advection equation
On the rate of convergence in periodic homogenization of scalar first-order ordinary differential equations
![QR code for arXiv:1408.0820 [math.AP]](http://oss.arxitics.com/images/favicon.svg)