FE-BE coupling for a transmission problem involving microstructure

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