ON THE SYMMETRICAL BOUNDARY-ELEMENT METHOD AND THE SYMMETRICAL COUPLING OF BOUNDARY ELEMENTS AND FINITE-ELEMENTS

The finite element method and the boundary element method are among th e most frequently applied tools in the numerical treatment of partial differential equations. However, their properties appear to be complem entary: white the boundary element method is appropriate for the most important linear partial differential equations with constant coeffici ents in bounded or unbounded domains, the finite element method seems to be more appropriate for inhomogeneous or even nonlinear problems; b ut is somehow restricted to bounded domains. The symmetric coupling of the two methods inherits the advantages of both methods. This paper t reats the symmetric coupling of finite elements and boundary elements for a model transmission problem in two and three dimensions where we have two domains: a bounded domain with nonlinear, even plastic materi al behaviour, is surrounded by an unbounded, exterior, domain with iso tropic homogeneous linear elastic material. Practically, the coupling is performed such that the boundary element method contributes a macro -element, like a large finite element, within a standard finite elemen t analysis program. Emphasis is on two-dimensional problems where the approach using the Poincare-Steklov operator seems to be impossible at first glance.