Many physical materials of practical relevance can attain several variants
of crystalline microstructure. The appropriate energy functional is necessa
rily nonconvex, and the minimization of the functional becomes a challengin
g problem. A new numerical method based on discontinuous finite elements an
d a scaled energy functional is proposed. It exhibits excellent convergence
behavior for the energy (second order) as well as other crucial quantities
of interest for general spatial meshes, contrary to standard (non-)conform
ing methods. Both theoretical analyses and numerical test calculations are
presented and contrasted to other current finite element methods for this p
roblem.