On the inf-sup condition for hierarchical model reduction of the Stokes problem with Dirichlet inflow boundary conditions
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Hierarchical Model Reduction (HiMod) is a discretization method that allows to reduce a 3D/2D problem exhibiting a main directionality (such as flows in pipelines) to a system of coupled 1D problems [1]. HiMod relies on a separation of variables, and discretizes the leading and the transverse directions in a different way: in particular, the transverse direction is resolved through a customized modal basis [2], while the leading direction is approximated by a standard finite element method on a 1D mesh. In this presentation we discuss recent advancements in the theoretical foundations of HiMod for fluid dynamics problems by establishing a rigorous rule to select the HiMod approximation (in particular, the number of modes for velocity and pressure) in order to guarantee the inf-sup stability of the HiMod discretization.