  We develop a stabilized cut discontinuous Galerkin framework for the
numerical solution of el- liptic boundary value and interface problems on
complicated domains. The domain of interest is embedded in a structured,
unfitted background mesh in R d , so that the boundary or interface can cut
through it in an arbitrary fashion. The method is based on an unfitted variant
of the classical symmetric interior penalty method using piecewise
discontinuous polynomials defined on the back- ground mesh. Instead of the cell
agglomeration technique commonly used in previously introduced unfitted
discontinuous Galerkin methods, we employ and extend ghost penalty techniques
from recently developed continuous cut finite element methods, which allows for
a minimal extension of existing fitted discontinuous Galerkin software to
handle unfitted geometries. Identifying four abstract assumptions on the ghost
penalty, we derive geometrically robust a priori error and con- dition number
estimates for the Poisson boundary value problem which hold irrespective of the
particular cut configuration. Possible realizations of suitable ghost penalties
are discussed. We also demonstrate how the framework can be elegantly applied
to discretize high contrast interface problems. The theoretical results are
illustrated by a number of numerical experiments for various approximation
orders and for two and three-dimensional test problems.
