A weak Galerkin finite-element method for singularly perturbed convection-diffusion-reaction problems with interface

In this paper, a weak Galerkin (WG) finite-element method is developed and analyzed for singularly perturbed convection-diffusion-reaction problems with interface. The WG algorithm is very simple in terms of variational formulation and has less unknowns. This algorithm allows us to use finite-element partitions with general polytopal meshes and is also easily generalizable to higher orders. This method can accommodate very complicated interfaces because of its high flexibility in choosing the finite-element partitions. Optimal order error estimate is established for the WG approximations in discrete H1 norm. Numerical experiments are presented to confirm our theoretical finding and to show efficiency, flexibility, accuracy and robustness of the WG interface approach.