Finite element analysis of microstructure for the cubic to tetragonal transformation

Martensitic crystals which can undergo a cubic to tetragonal phase transformation have a nonconvex energy density with three symmetry-related, rotationally invariant energy wells. We give estimates for the numerical approximation of a first-order laminate for such martensitic crystals. We give bounds for the L² convergence of directional derivatives in the "twin" plane, for the L² convergence of the deformation, for the weak convergence of the deformation gradient, for the convergence of the microstructure, and for the convergence of nonlinear integrals of the deformation gradient.