Convergence of variational approximation schemes for elastodynamics with polyconvex energy
نویسندگان
چکیده
We consider a variational scheme developed by S. Demoulini, D. M. A. Stuart and A. E. Tzavaras [Arch. Rat. 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 L-theory bounds, and provides an error estimate for the approximation before the formation of shocks. keywords: nonlinear elasticity, polyconvexity, variational approximation scheme. AMS Subject Classification: 35L70 74B20 74H20
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