Local effects in engineering with macro-elements Original Research Article

he presented strategy for coupling the Finite Element Method and the Boundary Element Method is based on a hybrid formulation for the trial and test functions. The usual variational formulation of the problem for the whole domain Ω is extended by a coupling equation, using a second bilinear form for the BE substructures. This offers the possibility to construct a two grid method with different discretization parameters for the FE- and the BE-substructures. The properties of the coupling operator like symmetry and positive definiteness are guaranteed only on the continuous level. An essential feature of the proposed method is the realization of these properties also on the discrete approximation level with an a priori defined accuracy. This is carried out in an adaptive scheme by expanding the Poincaré-Steklov operator on the BE-substructures in a Neumann series and defining error indicators for the construction of the discrete coupling operator. The proposed FE/BE-technique handles in particular stress concentration problems very efficiently, providing a locally high resolution of the investigated stress field.