A new stabilized finite element formulation for scalar convection–diffusion problems: the streamline and approximate upwind/Petrov–Galerkin method

Abstract

A new stabilized and accurate finite element formulation for convection-dominated problems is herein developed. The basis of the new formulation is the choice of a new upwind function. The upwind function chosen for the new method provokes its degeneration into the SUPG or CAU methods, depending on the approximate solution’s regularity. The accuracy and stability of the new formulation for the linear and scalar advection–diffusion equation is demonstrated in several numerical examples.