00682nas a2200145   4500008004100000245009900041210006900140260001000209520018600219100001700405700002000422700002200442700002100464856005100485       2015                        en  d00aSupremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations0 aSupremizer stabilization of PODGalerkin approximation of paramet  bWiley3 aIn this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number.1 aBallarin, F.1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi  uhttp://urania.sissa.it/xmlui/handle/1963/3470101619nas a2200145   4500008004100000245010700041210006900148260001300217520111600230100001701346700002001363700002101383700001801404856005101422       2014                        en  d00aShape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows0 aShape Optimization by FreeForm Deformation Existence Results and  bSpringer3 aShape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature.1 aBallarin, F.1 aManzoni, Andrea1 aRozza, Gianluigi1 aSalsa, Sandro  uhttp://urania.sissa.it/xmlui/handle/1963/34698