On stabilized finite element formulations for incompressible advective-diffusive transport and fluid flow problems

A new approach is presented to obtain stabilized finite element formulation s such as streamline-upwind/Petrov-Galerkin (SUPG) and Galerkin-least-squar es (GLS). The procedure consists in modifying the equations to be solved an d then obtaining the variational equations by the standard Galerkin method. The new formulation generates additional terms involving boundary integral s to standard stabilization techniques. These terms compensate for the lack of consistency of the traditional SUPG and GLS methods for which stabiliza tion terms are added only on the element interiors, while jumps of the resi dual across element faces are neglected. A physical interpretation is provi ded of how the modified equations are obtained. It is shown how stabilized formulations such as streamline-upwind (SU) and SUPC are recovered as speci al cases. Stabilization terms defined on the element interiors are always a ccompanied by additional boundary integrals, The presence of the boundary i ntegrals is shown to improve the numerical prediction for various viscous a nd nearly inviscid flows. (C) 2000 Elsevier Science S.A. All rights reserve d.