In the past a number of coupling ideas have been introduced in order to combine the different characteristics of the boundary and the finite element method. Considering the practical use of the method, scientists have come to the result that - contrary to many formulations - coupling did not work in a satisfactory manner. This paper presents a new kernal idea for two- and three-dimensional problems: On the basis of Schnack & Turke, uniqueness and existence of the weak formulation of the proposed coupling procedure can be shown. The arguments resemble those given by Brezzi & Johnson. Moreover, together with Céa's lemma, an asymptotic estimate of optimal order for the global error can be achieved (cf. Hsiao, Schnack & Wendland). Thus a high accuracy for the discrete system can be realized in a low CPU-time, and - what is most important - the accuracy of the coupling operator can be controlled, i.e. the definiteness and the symmetry of the coupling operator. Some computational results of elasticity will demonstrate the practical use of the formulation.

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