Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

MT2014

Convergence of variational approximation schemes for three dimensional elastodynamims with polyconvex energy

​A. Miroshnikov, A.E. Tzavaras, Convergence of variational approximation schemes for three dimensional elastodynamims with polyconvex energy, J. Analysis Appl. (ZAA) 33 (2014), 43-64
A. Miroshnikov, A.E. Tzavaras
Nonlinear elasticity, polyconvexity, variational approximation scheme
2014
​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 Lp-theory bounds, and provides an error estimate for the approximation before the formation of shocks