A variational theorem for the scattering of steady elastic waves from inclusions (Q1148136)

The paper is rather lapidary, both in its physical volume and in the results formulated therein. A certain variational principle for the problem of steady state scattering of elastic waves by an inclusion embedded in an infinite homogeneous medium is presented for a class of kinematically admissible displacements. This principle is intended for utilization in the process of numerical solution of the problem by finite element method, namely by the so-called global-local finite elements, which combine standard elements and functions with global support. To formulate the variational principle the displacement field is assumed to possess several properties, such as smoothness, certain asymptotic behaviour, and some others. Then a special functional is defined and it is stated that it assumes a stationary value for the solution of the problem. The proof of the theorem is not provided ''... since it is readily constructed...'', according to the authors.