  Design optimization and uncertainty quantification, among other applications
of industrial interest, require fast or multiple queries of some parametric
model. The Proper Generalized Decomposition (PGD) provides a separable
solution, a \emph{computational vademecum} explicitly dependent on the
parameters, efficiently computed with a greedy algorithm combined with an
alternated directions scheme and compactly stored. This strategy has been
successfully employed in many problems in computational mechanics. The
application to problems with saddle point structure raises some difficulties
requiring further attention. This article proposes a PGD formulation of the
Stokes problem. Various possibilities of the separated forms of the PGD
solutions are discussed and analyzed, selecting the more viable option. The
efficacy of the proposed methodology is demonstrated in numerical examples for
both Stokes and Brinkman models.
