On the choice of a stabilizing subgrid for convection-diffusion problems

SUPG and Residual-Free Bubbles are closely related methods that have been used with success to stabilize a certain number of problems, including advection-dominated flows. In recent times, a slightly different idea has been proposed: to choose a suitable subgrid in each element, and then solving Standard Galerkin on the Augmented Grid. For this, however, the correct location of the subgrid node(s) plays a crucial role. Here, for the model problem of linear advection-diffusion equations, we propose a simple criterion to choose a single internal node such that the corresponding plain-Galerkin scheme on the augmented grid provides the same a priori error estimates that are typically obtained with SUPG or RFB methods.