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We consider a variational scheme developed by S. Demoulini, D. M. A. Stuartand A. E. Tzavaras [Arch. Ration. Mech. Anal. 157 (2001)] that approximates theequations of three dimensional elastodynamics with polyconvex stored energy. Weestablish the convergence of the time-continuous interpolates constructed inthe scheme to a solution of polyconvex elastodynamics before shock formation.The proof is based on a relative entropy estimation for the time-discreteapproximants in an environment of Lp-theory bounds, and provides an errorestimate for the approximation before the formation of shocks.

Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy