In the Reduced Basis approximation of Stokes and Navier-Stokes problems, the Galerkin projection on the reduced spaces does not necessarily preserved the inf-sup stability even if the snapshots were generated through a stable full order method. Therefore, in this work we aim at building a stabilized Reduced Basis (RB) method for the approximation of unsteady Stokes and Navier-Stokes problems in parametric reduced order settings. This work extends the results presented for parametrized steady Stokes and Navier-Stokes problems in a work of ours \cite{Ali2018}. We apply classical residual-based stabilization techniques for finite element methods in full order, and then the RB method is introduced as Galerkin projection onto RB space. We compare this approach with supremizer enrichment options through several numerical experiments. We are interested to (numerically) guarantee the parametrized reduced inf-sup condition and to reduce the online computational costs.

翻译：在斯托克斯和纳维耶-斯托克斯问题降低基准近似值中,关于缩小空间的Galerkin预测不一定能够保持上升的稳定性,即使光谱是通过稳定的完整顺序方法生成的。因此,在这项工作中,我们的目标是为不稳定的斯托克斯和纳维耶-斯托克斯近近近近值问题建立一个稳定的降低基准(RB)方法。这项工作扩展了在我们的工程\cite{Ali2018}中出现的关于平衡稳定的斯托克斯和纳维耶-斯托克斯问题的结果。我们采用了传统的基于残余的稳定技术来使用有限的元素方法,然后将RB方法作为Galerkin投射到RB空间。我们通过几个数字实验将这一方法与最精美的浓缩选项进行比较。我们有兴趣(以数字方式)保证(以数字方式)保证节均的下降,并降低在线计算成本。