Petrov-Galerkin and Galerkin/Least Squares stabilized approaches for advectivediffusive transport problems

Abstract

[Abstract] The Finite Element method with a Galerkin type weighting is a straight-forward weighted residual method that has been sucessfuly used in many engineering applications, specially in Solid Mechanics. However, this method yields oscillatory solutions when it is applied to high-advective problems in Fluid Mechanics. Several stabilized numerical formulations have been proposed in the last years to overcome these inestabilities. The common methodology of most of these approaches is based on the addition of a term to the Galerkin formulation, in order to enhance the estability behaviour while preserving the weighting residual scheme. In this paper, we focus our attention in the Stream Upwind/Petrov Galerkin method (SUPG), and the Galerkin/least-squares method (GLS). We will review the mathematical formulation of both of them, as well as the key concept of their respective fundamentals and derivations, i.e. the exact artificial diffusion method for the SUPG and the Least Squares Finite Element method for the GLS. Finally, we will present a comparision between both methods, pointing out important coincidences and estabishing their mutual relations.