We analyze a finite element/boundary element procedure to solve a non-convex
contact problem for the double-well potential. After relaxing the associated
functional, the degenerate minimization problem is reduced to a boundary/domain
variational inequality, a discretized saddle point formulation of which may
then be solved numerically. The convergence of the Galerkin approximations to
certain macroscopic quantities and a corresponding a posteriori estimate for
the approximation error are discussed.