Numerical analysis of nonconvex minimization problems allowing microstructures

The numerical computation of nonconvex variational problems, e.g., appearing in the modelling of microstructure in crystals, faces the approximation of high oscillations. Although these oscillatory discrete minimizers are properly related to corresponding Young measures they are costly and difficult to compute. To support this, we prove in this paper that, for a model problem, there is a cluster of local minimizers around any global discrete minimizer.