  In this paper, we derive a priori error estimates for a class of interior
penalty discontinuous Galerkin (DG) methods using immersed finite element (IFE)
functions for a classic second-order elliptic interface problem. The error
estimation shows that these methods can converge optimally in a mesh-dependent
energy norm. The combination of IFEs and DG formulation in these methods allows
local mesh refinement in the Cartesian mesh structure for interface problems.
Numerical results are provided to demonstrate the convergence and local mesh
refinement features of these DG-IFE methods.
