On the choice of stabilizing sub-grid for convection diffusion problem on rectangular grids

A stabilizing sub-grid which consists of a single additional node in each rectangular element is analyzed for solving the convection diffusion problem, especially in the case of small diffusion. We provide a simple recipe for spotting the location of the additional node that contributes a very good stabilizing effect to the overall numerical method.Wefurther study convergence properties of the method under consideration and prove that the standard Galerkin finite element solution on augmented grid produces a discrete solution that satisfies the same type of a priori error estimates that are typically obtained with the SUPG method. Some numerical experiments that confirm the theoretical findings are also presented.