  In this work, we analyze an unfitted discontinuous Galerkin discretization
for the numerical solution of the Stokes system based on equal higher-order
discontinuous velocities and pressures. This approach combines the best from
both worlds, firstly the advantages of a piece-wise discontinuous high-order
accurate approximation and secondly the advantages of an unfitted to the true
geometry grid around possibly complex objects and/or geometrical deformations.
Utilizing a fictitious domain framework, the physical domain of interest is
embedded in an unfitted background mesh and the geometrically unfitted
discretization is built upon symmetric interior penalty discontinuous Galerkin
formulation. To enhance stability we enrich the discrete variational
formulation with a pressure stabilization term. Moreover, the present
contribution adopts high order ghost penalty strategies to address the ill
conditioning of the system matrix caused by small truncated elements with
respect to the unfitted boundary. Motivated by continuous unfitted FEM
[21,74,75] along with other unfitted mesh surveys grounded on discontinuous
spaces [10,44,45,73], we use proper velocity and pressure ghost penalties
defined on faces of cut cells to establish a robust high-order method, in spite
of the cell agglomeration technique usually applied on dG methods. The current
presentation should prove valuable in engineering applications where special
emphasis is placed on the optimal effective approximation attaining much
smaller relative errors in coarser meshes. Inf-sup stability, the optimal order
of convergence, and the condition number sensitivity with respect to cut
configuration are investigated. Numerical examples verify the theoretical
results.
