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arXiv · 1408.0820

Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy

Alexey Miroshnikov·Athanasios E. Tzavaras
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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)] 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.

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Alexey Miroshnikov, Athanasios E. Tzavaras. 2014-08-04. Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy. https://doi.org/10.4171/zaa%2F1498

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