THE H-P VERSION OF THE COUPLING OF FINITE-ELEMENT AND BOUNDARY-ELEMENT METHODS FOR TRANSMISSION PROBLEMS IN POLYHEDRAL DOMAINS

This paper analyzes the rate of convergence of the h-p version of the coupling of the finite element and boundary element method for transmi ssion problems with a linear differential operator with variable coeff icients in a bounded polyhedral domain Omega(1) and with constant coef ficients in the exterior domain Omega(2) = R-3\<(Omega)over bar>1. Thi s procedure uses the variational formulation of the differential equat ion in Omega(1) and involves integral operators on the interface betwe en Omega(1) and Omega(2). The finite elements are used to obtain appro ximate solutions of the differential equation in Omega(1) and the boun dary elements are used to obtain approximate solutions of the integral equations. For given piecewise analytic data we show that the Galerki n solution of this coupling procedure converges exponentially fast in the energy norm if the h-p version is used both for finite elements an d boundary elements.