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We analyze a discontinuous Galerkin FEM–BEM scheme for a second order elliptic transmission problem posed in the three-dimensional space. The symmetric variational formulation is discretized by nonconforming Raviart–Thomas finite elements on a general partition of the interior domain coupled with discontinuous boundary elements on an independent quasi-uniform mesh of the transmission interface. We prove (almost) quasi-optimal convergence of the method and confirm the theory by a numerical experiment. In addition we consider the case when continuous rather than discontinuous boundary elements are used.

Symmetric Coupling of LDG–FEM and DG–BEM