An a priori error estimate for finite element discretizations in nonlinear elasticity for polyconvex materials under small loads

Summary.We prove optimal a priori error estimates in W1,p for finite element minimizers of polyconvex energy functionals with small applied loads. The proof relies on a quantitative version of Zhang’s stability estimate (K. Zhang, Arch. Rat. Mech. Anal. 114 (1991), 95-117).