  We develop a cut Discontinuous Galerkin method (cutDGM) for a
diffusion-reaction equation in a bulk domain which is coupled to a
corresponding equation on the boundary of the bulk domain. The bulk domain is
embedded into a structured, unfitted background mesh. By adding certain
stabilization terms to the discrete variational formulation of the coupled
bulk-surface problem, the resulting cutDGM is provably stable and exhibits
optimal convergence properties as demon- strated by numerical experiments. We
also show both theoretically and numerically that the system matrix is
well-conditioned, irrespective of the relative position of the bulk domain in
the background mesh.
