On stabilized finite element formulations for incompressible flows

A new approach is presented to obtain stabilized finite element formulations such as SUPG and GLS. The procedure consists in modifying the equations to be solved and then to obtain the variational equations by a standard Galerkin method. The new formulation adds terms involving boundary integrals to the standard stabilization techniques. These terms compensate for a 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 neglegted. A physical interpretation is provided of how the modified equations are obtained. It is shown how stabilized formulations such as SU, SUPG and GLS are recovered. In all cases stabilization terms defined on the element interiors are 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. Finally, the present approach is directly applicable to higher order finite element discretizations.

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