Numerical Approximation of the Solution of a Variational Problem with a DoubleWall Potential

摘要

Variational problems with a double well potential are not lower semicontinuousand can have oscillations. However, the gradients do converge in the weak topology, i.e., their local spatial averages converge. Such functionals arise in the description of equilibria of crystals or other ordered materials. Stable configurations for solid crystals which have symmetry-related to the oscillations that energy minimizing sequences for the bulk energy exhibit. An analysis is given of approximation methods for variational problems with a double well potential to give a rigorous justification for the use of such numerical methods to model the behavior of this class of solid crystals. Finite element method, error estimates, numerical approximation nonconvex variational problem, crystals, shape memory materials.