  In this paper, we present an immersed weak Galerkin method for solving
second-order elliptic interface problems. The proposed method does not require
the meshes to be aligned with the interface. Consequently, uniform Cartesian
meshes can be used for nontrivial interfacial geometry. We show the existence
and uniqueness of the numerical algorithm, and prove the error estimates for
the energy norm. Numerical results are reported to demonstrate the performance
of the method.
