On stabilized finite element formulations for incompressible advective–diffusive transport and fluid flow problems Original Research Article

A new approach is presented to obtain stabilized finite element formulations such as streamline-upwind/Petrov–Galerkin (SUPG) and Galerkin-least-squares (GLS). The procedure consists in modifying the equations to be solved and then obtaining the variational equations by the standard Galerkin method. The new formulation generates additional terms involving boundary integrals to standard stabilization techniques. These terms compensate for the lack of consistency of the traditional SUPG and GLS methods for which stabilization terms are added only on the element interiors, while jumps of the residual across element faces are neglected. A physical interpretation is provided of how the modified equations are obtained. It is shown how stabilized formulations such as streamline-upwind (SU) and SUPG are recovered as special cases. Stabilization terms defined on the element interiors are always accompanied by additional boundary integrals. The presence of the boundary integrals is shown to improve the numerical prediction for various viscous and nearly inviscid flows.