  This paper proposes an interface/boundary-unfitted eXtended hybridizable
discontinuous Galerkin (X-HDG) method for Darcy-Stokes-Brinkman interface
problems in two and three dimensions. The method uses piecewise linear
polynomials for the velocity approximation and piecewise constants for both the
velocity gradient and pressure approximations in the interior of elements
inside the subdomains separated by the interface, uses piecewise constants for
the numerical traces of velocity on the inter-element boundaries inside the
subdomains, and uses piecewise constants or linear polynomials for the
numerical traces of velocity on the interface. Optimal error estimates are
derived for the interface-unfitted X-HDG scheme. Numerical experiments are
provided to verify the theoretical results and the robustness of the proposed
method.
