Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2013-12-27
Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex EnergyAlexey Miroshnikov and Athanasios E. Tzavaras (1) University of Maryland, College Park, USA
(2) University of Crete, Heraklion, Greece
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 $L^p$-theory bounds, and provides an error estimate for the approximation before the formation of shocks.
Keywords: Nonlinear elasticity, polyconvexity, variational approximation scheme
Miroshnikov Alexey, Tzavaras Athanasios: Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy. Z. Anal. Anwend. 33 (2014), 43-64. doi: 10.4171/ZAA/1498