Numerical analysis of oscillations in multiple well problems

Summary.

Variational problems which fail to be convex occur often in the study of ordered materials such as crystals. In these problems, the energy density for the material has multiple potential wells. In this paper, we study multiple well problems by first, determining the analytic properties of energy minimizing sequences and then, by estimating the continuous problem by an approximation using piecewise linear finite elements. We show that even when there is no minimizer of the energy, the approximations still take on a predictable structure.