Symmetric coupling of LDG-FEM and DG-BEM

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.